Here are all titles and abstracts we have received so far...
Vincenzo
Alba (Talk)
Title: Entanglement spectroscopy of SU(2)-broken phases in two dimensions
Abstract: In magnetically ordered systems the breaking of SU(2) symmetry in the thermodynamic limit is associated with the appearance of a special type of low-lying excitations in finite size energy spectra, the so-called tower of states (TOS). In this talk I will provide numerical evidence that there is a correspondence between the SU(2) tower of states and the lower part of the ground state entanglement spectrum (ES). In particular, I will present state-of-the-art DMRG calculations for the 2D antiferromagnetic J1-J2 Heisenberg model on both the triangular and Kagome lattice. At large ferromagnetic J2 the model exhibits a magnetically ordered ground state. Correspondingly, its ES contains a family of low-lying levels that are reminiscent of the energy tower of states. Their behaviour (level counting, finite size scaling in the thermodynamic limit) sharply reflects tower of states features, and is characterized in terms of an effective entanglement Hamiltonian. At large system sizes TOS levels are divided from the rest by an entanglement gap.
Tillmann Baumgratz (Talk)
Title: Efficient State Tomography with Matrix Product Structures
Abstract: The ability to store and manipulate interacting quantum many-body systems, such as linearly arranged ions in ion traps, enhanced rapidly during the last years. By now, the number of controllable particles in such systems has reached sizes for which conventional methods of quantum tomography fail due to both the limited time that is realistically available for the experiment and the limitations to the resources that are available for the classical post-processing of the experimental data. We show that a vast majority of physically interesting quantum states on one-dimensional lattices is uniquely determined by local information and further, that these states may efficiently be reconstructed from their reduced density matrices.
Sougato Bose (Talk)
Title: Entanglement Spectrum and Negativity for Illuminating Impurity Models
Abstract: We will exemplify the usage of measures from quantum information in revealing the structure of entangled ground states of many-body systems. We will particularly focus on many-body models with impurities and their quantum phase transitions. First, we show how the use of negativity can give one the extent of the elusive Kondo cloud in a spin chain emulation of Kondo physics. We also show how readily such information can be exploited for a non equilibrium dynamics that generates a quantum router with two Kondo spin chains. Next, we explore how the quantum phase transition in a two impurity Kondo-RKKY model can be captured by entanglement measures. Finally, we show how the Schmidt gap, which stems from the entanglement spectrum, can provide an order parameter for the Kondo-RKKY quantum phase transition which was so far lacking. Though the Schmidt gap is a non-local observable, it scales just as the order parameter in the Kondo-RKKY quantum phase transition.
Peter Bröcker (Poster)
Title: Entanglement Entropy for Many-Fermion Systems
Abstract: The precise determination of the entanglement of interacting quantum many-body systems is now appreciated as an indispensable tool to identify the fundamental character of the ground state of such systems. This is particularly true for unconventional ground states harbouring non-local topological order or so-called quantum spin liquids that evade a standard description in terms of correlation functions.
With the entanglement entropy emerging as one of the central measures of entanglement, recent progress has focused on a precise characterization of its scaling behaviour, in particular in the determination of (subleading) corrections to the prevalent boundary-law. While much progress has been made for spin and bosonic quantum many-body systems, fermion systems have proved to be more difficult.
For a large class of interacting fermionic systems, the numerical method of choice for unbiased, large-scale simulations is Determinantal Quantum Monte Carlo (DQMC) for which a generalization of the replica techniques developed to calculate entanglement entropies for spin and bosonic systems has remained an open question. Here we show one possibility how to construct the corresponding algorithm in DQMC and demonstrate its strength by studying the one-dimensional Hubbard systems. We also compare our results to another recent approach based on free fermion Green’s functions.
Boye Buyens (Poster)
Title: Matrix Product States: (1+1)-D Quantum Electrodynamics
Abstract: The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavour quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground state. With the ground state we could study elementary one-particle excitations in the continuum limit, string breaking and real-time evolution of the system induced by a quench in the form of a uniform background electric field.
Pasquale Calabrese (Talk)
Title: Entanglement negativity and quantum field theory
Abstract: I will present systematic methods to calculate the entanglement negativity in the ground state of 1+1 dimensional quantum field theories, with particular emphasis on conformal invariant ones. This is based on a path integral construction of the partial traspose of the reduced density matrix and of its replicated traces.
John Cardy (Talk)
Title: Expectation values in eigenstates of the reduced density matrix
Abstract: Numerical methods like DMRG truncate the reduced density matrix, breaking translation invariance and making it difficult to measure correlation functions. It might be better to confront numerical data with theoretical expectations of how these should behave in the truncated subspace. Some of these expectations are presented here.
Philip Crowley (Poster)
Title: Quantum and Classical in Adiabatic Quantum Computation
Abstract: Adiabatic transport provides a powerful way to manipulate quantum states. By preparing a system in readily initialised state and then slowly changing its Hamiltonian, on may achieve quantum states that would otherwise be extremely difficult. Moreover, a judicious choice of final Hamiltonian whose ground state encodes the solution to a problem allows adiabatic transport to be used for universal quantum computation. However, the dephasing effects of the environment limit the quantum correlations that an open system can support and degrade the power of such adiabatic computation. We quantify this effect by allowing the system to evolve over a restricted set of quantum states, providing a link between physically inspired classical optimisation algorithms and quantum adiabatic optimisation. This new perspective allows us to develop benchmarks to bound the quantum correlations harnessed by an adiabatic computation. We use this to develop a set of tests aimed at quantifying the quantum resources required to perform different adiabatic quantum computations. Following recent interest in the D-Wave computer we apply this approach to the D-Wave Vesuvius machine with revealing - though inconclusive - results.
Benoit Descamps (Poster)
Title: Asymptotically decreasing Lieb-Robinson velocity for a class of dissipative quantum dynamics
Abstract: We study the velocity of the propagation of information for a class of local dissipative quantum dynamics. This finite velocity is expressed by the so-called Lieb-Robinson bound. Besides the properties of the already studied dynamics, we consider an additional relation that expresses the propagation of certain subspaces. The previously derived bounds did not reflect the dissipative character of the dynamics and yielded the same result as for the reversible case. In this poster, we show that for this class the velocity of propagation of information is time dependent and decays in time towards a smaller velocity. In some cases the velocity becomes zero.
Elisa Ercolessi (Talk)
Title: Dynamics of entanglement crossing a quantum phase transition
Abstract: We discuss the time evolution of bipartite quantities in a finite-size system which crosses a quantum phase transition, focusing on the Ising model in a time-dependent magnetic field which is linearly tuned on a time scale τ. We consider the dynamics of the half-chain entanglement entropy and entanglement spectrum for different ranges of τ. Moreover, we investigate the Kibble-Zurek mechanism, through the scaling of the entanglement entropy and the Schmidt gap.
Fabian Essler (Talk)
Title: Shell-filling effect in the entanglement entropies of spinful fermions
Abstract: I consider the von Neumann and Rényi entropies of the one dimensional quarter-filled Hubbard model. For periodic boundary conditions the entropies exhibit an unexpected dependence on system size: for L = 4 mod 8 the results are in agreement with expectations based on conformal field theory, while for L = 0 mod 8 additional contributions arise. I explain this observation in terms of a shell-filling effect, and develop a conformal field theory approach to calculate the extra term in the entropies. Similar shell filling effects in entanglement entropies are expected to be present in higher dimensions and for other multicomponent systems. References: F.H.L. Essler, A. Läuchli and P. Calabrese, Phys. Rev. Lett. 110, 115701 (2013).
Fabio Franchini (Talk)
Title: Universal Quantum Simulator, Local Convertibility and Edge States in Many-body Systems
Abstract: In some many-body systems, certain ground state entanglement (Renyi) entropies increase even as the correlation length decreases. This entanglement non-monotonicity implies a stronger ``quantum nature" of the wave function and gives it a higher computational power, compared to classical manipulations. In this work we demonstrate that such a phenomenon, known as non-local convertibility, is due to the edge state (de)construction occurring in the system. To this end, we employ the example of the Ising chain, displaying an order-disorder quantum phase transition. Employing both analytical and numerical methods, we compute entanglement entropies for various system's bipartitions (A|B) and consider ground states with and without Majorana edge states. We find that the thermal ground states, enjoying the Hamiltonian symmetries, show non-local convertibility if either A or B are smaller than, or of the order of, the correlation length. In contrast, the ordered (symmetry breaking) ground state is always locally convertible. The edge states behavior explains all these results and could disclose a paradigm to understand local convertibility in other quantum phases of matter. The connection we establish between convertibility and non-local, quantum correlations provides a clear criterion of which features a universal quantum simulator should possess to outperform a classical machine.
Johannes Helmes (Poster)
Title: Topological entropies for the toric code in a magnetic field
Abstract: Although the concept of topological order – long-range order beyond the conventional paradigm of symmetry broken order – has been introduced more than two decades ago, its unambiguous identification and quantitative characterization has remained a challenging task for both theory and experiment.
Since long-range quantum mechanical entanglement is a key factor in forming this peculiar order, it is natural to look for fingerprints of topological order in various measures of entanglement. Much progress has recently been achieved by carefully investigating entanglement entropies like the von Neumann or the Renyi entropies, which expose the precious information on long-range entanglement in their scaling behavior. Particularly the Renyi entropies have received much attention from the numerical community due to their accessibility in quantum Monte Carlo simulations. On this poster, we present a quantum Monte Carlo method to calculate Renyi entropies for a prototypical lattice model harboring a non-trivial topological phase – the toric code model augmented by a magnetic field. Using stochastic series expansion techniques we calculate the topological corrections to the entanglement entropies for various field strengths, which allows us to unambiguously track the topological phase up to a quantum phase transition into a trivial phase.
Jesper Jacobsen (Talk)
Title: Entanglement in gapless systems with a quantum impurity
Abstract: We consider the entanglement between two one-dimensional quantum wires (Luttinger Liquids) coupled by tunneling through a quantum impurity. The physics of the system involves a crossover between weak and strong coupling regimes characterized by an energy scale TB, and methods of conformal field theory therefore cannot be applied. The evolution of the entanglement in this crossover has led to many numerical studies, but has remained little understood, analytically or even qualitatively. We argue in this Letter that the correct universal scaling form of the entanglement entropy S (for an arbitrary interval of length L containing the impurity) is ∂S/∂lnL=f(LTB). In the special case where the coupling to the impurity can be refermionized, we show how the universal function f(LTB) can be obtained analytically using recent results on form factors of twist fields and a defect massless-scattering formalism. Our results are carefully checked against numerical simulations.
Antony Lee (Poster)
Title: Gaussian state dynamics: An application to quantum field theory
Abstract: Quantum field theory in its most common form looks at the interaction between fields via perturbation theory. While this has given us great insight and theoretical predictions, non-perturbative approaches are still the focus of much attention and highly sought after. Here we describe a model to investigate two linearly coupled Klein-Gordon fields when the initial states are Gaussian. We use the Bosonic and quadratic nature of the Hamiltonian to solve its dynamics exactly using ideas from Symplectic geometry.
Francesco Ravanini (Talk)
Title: Entanglement entropy of non unitary conformal field theory
Abstract: We show that the entanglement entropy of a region of large size L in a one-dimensional non-unitary critical model behaves as ceff/3 log L, where ceff is the effective central charge. We also obtain results for models with boundaries, and with a large but nonzero correlation length. These results generalize the well known expressions for unitary models. We provide a general proof, as well as numerical evidence for a non-unitary spin chain and an analytical computation using the corner transfer matrix method for a non-unitary lattice model. We use a new algebraic technique for studying the branching that arise within the replica approach, and find a new expression for the entanglement entropy in terms of correlation functions of twist fields that is valid for non-unitary models. The talk is mainly based on the recent paper: Davide Bianchini, Olalla A. Castro-Alvaredo, Benjamin Doyon, Emanuele Levi and Francesco Ravanini, Entanglement Entropy of Non Unitary Conformal Field Theory, arXiv:1405.2804.
Hubert Saleur (Talk)
Title: Exact overlaps in the Kondo problem
Abstract: I will discuss an exact formula for the scalar product of ground states of the (anisotropic) Kondo model with different Kondo temperatures. The formula will be related, on the one hand, to the Anderson orthogonality catastrophe, and on the other, to the concept of `quantum Jost functions’. Applications to the calculation of various crossovers in quenched quantum impurity problems will also be discussed. This is work in progress with S. Lukyanov, J.L. Jacobsen and R. Vasseur.
German Sierra (Talk)
Title: Primes go Quantum
Abstract: Prime numbers are the building blocks of Arithmetics and therefore classical objects. However, they can be treated as quantum objects by superposing them in the computational basis of a quantum computer. In this talk we shall apply quantum information tools to create the Prime state, and to quantify its entanglement properties in terms of number theoretical functions.
Luca Taddia (Talk)
Title: Entanglement entropies in conformal systems with boundaries
Abstract: We study the entanglement entropies in one-dimensional open critical systems, whose effective description is given by a conformal field theory with boundaries. We show that for pure-state systems formed by the ground state or by the excited states associated to primary fields, the entanglement entropies have a finite-size behaviour that depends on the correlation of the underlying field theory. The analytical results are checked numerically, finding excellent agreement for the quantum chains ruled by the theories with central charge c=1/2 and c=1.
Erik Tonni (Talk)
Title: Entanglement entropies of many disjoint intervals in CFT
Abstract: The Renyi entropies of a generic number of disjoint intervals are considered for two conformal field theories: the free compactified boson and the Ising model. Analytic expressions are obtained by employing a particular class of Riemann surfaces. Some of the analytic predictions are checked against lattice results through exact diagonalization for the harmonic chain and through matrix product states computations for the critical Ising chain.
Laurens Vanderstraeten (Poster)
Title: S-matrix from matrix product states
Abstract: Matrix product states have shown to provide an excellent variational ansatz to capture the ground state properties of one-dimensional quantum systems. We use this formalism to study elementary excitations of these systems: we determine their dispersion relation, spectral weights and scattering properties. In this way we are able to construct, based on a microscopic description of the excitations and their interactions, an effective theory for the low-lying dynamical properties of quantum spin chains. arXiv reference: 1312.6793
Frank Verstraete (Talk)
TBA
Robert Weston (Talk)
Title: The Exact and Scaling Form of the Bipartite Fidelity of an Infinite XXZ Chain
Abstract: We study the 6-vertex model with a semi-infinite split by using the technology of the vertex-operator approach. We produce a general integral expression for correlation functions and specialise to find a simple exact expression for the bipartite fidelity f = |<vac|vac>'|^2, where |vac> is the vacuum eigenstate of an infinite-size antiferromagnetic XXZ chain and |vac>' is the vacuum eigenstate of an infinite-size XXZ chain which is split in two. We consider the quantity −log(f) which has been put forward as a measure of quantum entanglement, and show that the large correlation length ξ behaviour is consistent with a general conjecture −log(f) ~ c/8 log(ξ), where c is the central charge of the UV conformal field theory (with c = 1 for the XXZ chain). This behaviour is a natural extension of the existing conformal field theory prediction of −log(f) ~ c/8 log(L) for a length L bipartite system with 0 <L<ξ.
Zoltan Zimboras (Poster)
Title: Area law violation for the mutual information in a nonequilibrium steady state
Abstract: We study the nonequilibrium steady state of an infinite chain of free fermions, resulting from an initial state where the two sides of the system are prepared at different temperatures. The mutual information is calculated between two adjacent segments of the chain and is found to scale logarithmically in the subsystem size. This provides the first example of the violation of the area law in a quantum many-body system outside a zero temperature regime. The prefactor of the logarithm is obtained analytically and, furthermore, the same prefactor is shown to govern the logarithmic increase of mutual information in time, before the system relaxes locally to the steady state.
Published as V. Eisler and Z. Zimboras, Phys. Rev. A 89, 032321 (2014)
Title: Entanglement spectroscopy of SU(2)-broken phases in two dimensions
Abstract: In magnetically ordered systems the breaking of SU(2) symmetry in the thermodynamic limit is associated with the appearance of a special type of low-lying excitations in finite size energy spectra, the so-called tower of states (TOS). In this talk I will provide numerical evidence that there is a correspondence between the SU(2) tower of states and the lower part of the ground state entanglement spectrum (ES). In particular, I will present state-of-the-art DMRG calculations for the 2D antiferromagnetic J1-J2 Heisenberg model on both the triangular and Kagome lattice. At large ferromagnetic J2 the model exhibits a magnetically ordered ground state. Correspondingly, its ES contains a family of low-lying levels that are reminiscent of the energy tower of states. Their behaviour (level counting, finite size scaling in the thermodynamic limit) sharply reflects tower of states features, and is characterized in terms of an effective entanglement Hamiltonian. At large system sizes TOS levels are divided from the rest by an entanglement gap.
Tillmann Baumgratz (Talk)
Title: Efficient State Tomography with Matrix Product Structures
Abstract: The ability to store and manipulate interacting quantum many-body systems, such as linearly arranged ions in ion traps, enhanced rapidly during the last years. By now, the number of controllable particles in such systems has reached sizes for which conventional methods of quantum tomography fail due to both the limited time that is realistically available for the experiment and the limitations to the resources that are available for the classical post-processing of the experimental data. We show that a vast majority of physically interesting quantum states on one-dimensional lattices is uniquely determined by local information and further, that these states may efficiently be reconstructed from their reduced density matrices.
Sougato Bose (Talk)
Title: Entanglement Spectrum and Negativity for Illuminating Impurity Models
Abstract: We will exemplify the usage of measures from quantum information in revealing the structure of entangled ground states of many-body systems. We will particularly focus on many-body models with impurities and their quantum phase transitions. First, we show how the use of negativity can give one the extent of the elusive Kondo cloud in a spin chain emulation of Kondo physics. We also show how readily such information can be exploited for a non equilibrium dynamics that generates a quantum router with two Kondo spin chains. Next, we explore how the quantum phase transition in a two impurity Kondo-RKKY model can be captured by entanglement measures. Finally, we show how the Schmidt gap, which stems from the entanglement spectrum, can provide an order parameter for the Kondo-RKKY quantum phase transition which was so far lacking. Though the Schmidt gap is a non-local observable, it scales just as the order parameter in the Kondo-RKKY quantum phase transition.
Peter Bröcker (Poster)
Title: Entanglement Entropy for Many-Fermion Systems
Abstract: The precise determination of the entanglement of interacting quantum many-body systems is now appreciated as an indispensable tool to identify the fundamental character of the ground state of such systems. This is particularly true for unconventional ground states harbouring non-local topological order or so-called quantum spin liquids that evade a standard description in terms of correlation functions.
With the entanglement entropy emerging as one of the central measures of entanglement, recent progress has focused on a precise characterization of its scaling behaviour, in particular in the determination of (subleading) corrections to the prevalent boundary-law. While much progress has been made for spin and bosonic quantum many-body systems, fermion systems have proved to be more difficult.
For a large class of interacting fermionic systems, the numerical method of choice for unbiased, large-scale simulations is Determinantal Quantum Monte Carlo (DQMC) for which a generalization of the replica techniques developed to calculate entanglement entropies for spin and bosonic systems has remained an open question. Here we show one possibility how to construct the corresponding algorithm in DQMC and demonstrate its strength by studying the one-dimensional Hubbard systems. We also compare our results to another recent approach based on free fermion Green’s functions.
Boye Buyens (Poster)
Title: Matrix Product States: (1+1)-D Quantum Electrodynamics
Abstract: The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavour quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground state. With the ground state we could study elementary one-particle excitations in the continuum limit, string breaking and real-time evolution of the system induced by a quench in the form of a uniform background electric field.
Pasquale Calabrese (Talk)
Title: Entanglement negativity and quantum field theory
Abstract: I will present systematic methods to calculate the entanglement negativity in the ground state of 1+1 dimensional quantum field theories, with particular emphasis on conformal invariant ones. This is based on a path integral construction of the partial traspose of the reduced density matrix and of its replicated traces.
John Cardy (Talk)
Title: Expectation values in eigenstates of the reduced density matrix
Abstract: Numerical methods like DMRG truncate the reduced density matrix, breaking translation invariance and making it difficult to measure correlation functions. It might be better to confront numerical data with theoretical expectations of how these should behave in the truncated subspace. Some of these expectations are presented here.
Philip Crowley (Poster)
Title: Quantum and Classical in Adiabatic Quantum Computation
Abstract: Adiabatic transport provides a powerful way to manipulate quantum states. By preparing a system in readily initialised state and then slowly changing its Hamiltonian, on may achieve quantum states that would otherwise be extremely difficult. Moreover, a judicious choice of final Hamiltonian whose ground state encodes the solution to a problem allows adiabatic transport to be used for universal quantum computation. However, the dephasing effects of the environment limit the quantum correlations that an open system can support and degrade the power of such adiabatic computation. We quantify this effect by allowing the system to evolve over a restricted set of quantum states, providing a link between physically inspired classical optimisation algorithms and quantum adiabatic optimisation. This new perspective allows us to develop benchmarks to bound the quantum correlations harnessed by an adiabatic computation. We use this to develop a set of tests aimed at quantifying the quantum resources required to perform different adiabatic quantum computations. Following recent interest in the D-Wave computer we apply this approach to the D-Wave Vesuvius machine with revealing - though inconclusive - results.
Benoit Descamps (Poster)
Title: Asymptotically decreasing Lieb-Robinson velocity for a class of dissipative quantum dynamics
Abstract: We study the velocity of the propagation of information for a class of local dissipative quantum dynamics. This finite velocity is expressed by the so-called Lieb-Robinson bound. Besides the properties of the already studied dynamics, we consider an additional relation that expresses the propagation of certain subspaces. The previously derived bounds did not reflect the dissipative character of the dynamics and yielded the same result as for the reversible case. In this poster, we show that for this class the velocity of propagation of information is time dependent and decays in time towards a smaller velocity. In some cases the velocity becomes zero.
Elisa Ercolessi (Talk)
Title: Dynamics of entanglement crossing a quantum phase transition
Abstract: We discuss the time evolution of bipartite quantities in a finite-size system which crosses a quantum phase transition, focusing on the Ising model in a time-dependent magnetic field which is linearly tuned on a time scale τ. We consider the dynamics of the half-chain entanglement entropy and entanglement spectrum for different ranges of τ. Moreover, we investigate the Kibble-Zurek mechanism, through the scaling of the entanglement entropy and the Schmidt gap.
Fabian Essler (Talk)
Title: Shell-filling effect in the entanglement entropies of spinful fermions
Abstract: I consider the von Neumann and Rényi entropies of the one dimensional quarter-filled Hubbard model. For periodic boundary conditions the entropies exhibit an unexpected dependence on system size: for L = 4 mod 8 the results are in agreement with expectations based on conformal field theory, while for L = 0 mod 8 additional contributions arise. I explain this observation in terms of a shell-filling effect, and develop a conformal field theory approach to calculate the extra term in the entropies. Similar shell filling effects in entanglement entropies are expected to be present in higher dimensions and for other multicomponent systems. References: F.H.L. Essler, A. Läuchli and P. Calabrese, Phys. Rev. Lett. 110, 115701 (2013).
Fabio Franchini (Talk)
Title: Universal Quantum Simulator, Local Convertibility and Edge States in Many-body Systems
Abstract: In some many-body systems, certain ground state entanglement (Renyi) entropies increase even as the correlation length decreases. This entanglement non-monotonicity implies a stronger ``quantum nature" of the wave function and gives it a higher computational power, compared to classical manipulations. In this work we demonstrate that such a phenomenon, known as non-local convertibility, is due to the edge state (de)construction occurring in the system. To this end, we employ the example of the Ising chain, displaying an order-disorder quantum phase transition. Employing both analytical and numerical methods, we compute entanglement entropies for various system's bipartitions (A|B) and consider ground states with and without Majorana edge states. We find that the thermal ground states, enjoying the Hamiltonian symmetries, show non-local convertibility if either A or B are smaller than, or of the order of, the correlation length. In contrast, the ordered (symmetry breaking) ground state is always locally convertible. The edge states behavior explains all these results and could disclose a paradigm to understand local convertibility in other quantum phases of matter. The connection we establish between convertibility and non-local, quantum correlations provides a clear criterion of which features a universal quantum simulator should possess to outperform a classical machine.
Johannes Helmes (Poster)
Title: Topological entropies for the toric code in a magnetic field
Abstract: Although the concept of topological order – long-range order beyond the conventional paradigm of symmetry broken order – has been introduced more than two decades ago, its unambiguous identification and quantitative characterization has remained a challenging task for both theory and experiment.
Since long-range quantum mechanical entanglement is a key factor in forming this peculiar order, it is natural to look for fingerprints of topological order in various measures of entanglement. Much progress has recently been achieved by carefully investigating entanglement entropies like the von Neumann or the Renyi entropies, which expose the precious information on long-range entanglement in their scaling behavior. Particularly the Renyi entropies have received much attention from the numerical community due to their accessibility in quantum Monte Carlo simulations. On this poster, we present a quantum Monte Carlo method to calculate Renyi entropies for a prototypical lattice model harboring a non-trivial topological phase – the toric code model augmented by a magnetic field. Using stochastic series expansion techniques we calculate the topological corrections to the entanglement entropies for various field strengths, which allows us to unambiguously track the topological phase up to a quantum phase transition into a trivial phase.
Jesper Jacobsen (Talk)
Title: Entanglement in gapless systems with a quantum impurity
Abstract: We consider the entanglement between two one-dimensional quantum wires (Luttinger Liquids) coupled by tunneling through a quantum impurity. The physics of the system involves a crossover between weak and strong coupling regimes characterized by an energy scale TB, and methods of conformal field theory therefore cannot be applied. The evolution of the entanglement in this crossover has led to many numerical studies, but has remained little understood, analytically or even qualitatively. We argue in this Letter that the correct universal scaling form of the entanglement entropy S (for an arbitrary interval of length L containing the impurity) is ∂S/∂lnL=f(LTB). In the special case where the coupling to the impurity can be refermionized, we show how the universal function f(LTB) can be obtained analytically using recent results on form factors of twist fields and a defect massless-scattering formalism. Our results are carefully checked against numerical simulations.
Antony Lee (Poster)
Title: Gaussian state dynamics: An application to quantum field theory
Abstract: Quantum field theory in its most common form looks at the interaction between fields via perturbation theory. While this has given us great insight and theoretical predictions, non-perturbative approaches are still the focus of much attention and highly sought after. Here we describe a model to investigate two linearly coupled Klein-Gordon fields when the initial states are Gaussian. We use the Bosonic and quadratic nature of the Hamiltonian to solve its dynamics exactly using ideas from Symplectic geometry.
Francesco Ravanini (Talk)
Title: Entanglement entropy of non unitary conformal field theory
Abstract: We show that the entanglement entropy of a region of large size L in a one-dimensional non-unitary critical model behaves as ceff/3 log L, where ceff is the effective central charge. We also obtain results for models with boundaries, and with a large but nonzero correlation length. These results generalize the well known expressions for unitary models. We provide a general proof, as well as numerical evidence for a non-unitary spin chain and an analytical computation using the corner transfer matrix method for a non-unitary lattice model. We use a new algebraic technique for studying the branching that arise within the replica approach, and find a new expression for the entanglement entropy in terms of correlation functions of twist fields that is valid for non-unitary models. The talk is mainly based on the recent paper: Davide Bianchini, Olalla A. Castro-Alvaredo, Benjamin Doyon, Emanuele Levi and Francesco Ravanini, Entanglement Entropy of Non Unitary Conformal Field Theory, arXiv:1405.2804.
Hubert Saleur (Talk)
Title: Exact overlaps in the Kondo problem
Abstract: I will discuss an exact formula for the scalar product of ground states of the (anisotropic) Kondo model with different Kondo temperatures. The formula will be related, on the one hand, to the Anderson orthogonality catastrophe, and on the other, to the concept of `quantum Jost functions’. Applications to the calculation of various crossovers in quenched quantum impurity problems will also be discussed. This is work in progress with S. Lukyanov, J.L. Jacobsen and R. Vasseur.
German Sierra (Talk)
Title: Primes go Quantum
Abstract: Prime numbers are the building blocks of Arithmetics and therefore classical objects. However, they can be treated as quantum objects by superposing them in the computational basis of a quantum computer. In this talk we shall apply quantum information tools to create the Prime state, and to quantify its entanglement properties in terms of number theoretical functions.
Luca Taddia (Talk)
Title: Entanglement entropies in conformal systems with boundaries
Abstract: We study the entanglement entropies in one-dimensional open critical systems, whose effective description is given by a conformal field theory with boundaries. We show that for pure-state systems formed by the ground state or by the excited states associated to primary fields, the entanglement entropies have a finite-size behaviour that depends on the correlation of the underlying field theory. The analytical results are checked numerically, finding excellent agreement for the quantum chains ruled by the theories with central charge c=1/2 and c=1.
Erik Tonni (Talk)
Title: Entanglement entropies of many disjoint intervals in CFT
Abstract: The Renyi entropies of a generic number of disjoint intervals are considered for two conformal field theories: the free compactified boson and the Ising model. Analytic expressions are obtained by employing a particular class of Riemann surfaces. Some of the analytic predictions are checked against lattice results through exact diagonalization for the harmonic chain and through matrix product states computations for the critical Ising chain.
Laurens Vanderstraeten (Poster)
Title: S-matrix from matrix product states
Abstract: Matrix product states have shown to provide an excellent variational ansatz to capture the ground state properties of one-dimensional quantum systems. We use this formalism to study elementary excitations of these systems: we determine their dispersion relation, spectral weights and scattering properties. In this way we are able to construct, based on a microscopic description of the excitations and their interactions, an effective theory for the low-lying dynamical properties of quantum spin chains. arXiv reference: 1312.6793
Frank Verstraete (Talk)
TBA
Robert Weston (Talk)
Title: The Exact and Scaling Form of the Bipartite Fidelity of an Infinite XXZ Chain
Abstract: We study the 6-vertex model with a semi-infinite split by using the technology of the vertex-operator approach. We produce a general integral expression for correlation functions and specialise to find a simple exact expression for the bipartite fidelity f = |<vac|vac>'|^2, where |vac> is the vacuum eigenstate of an infinite-size antiferromagnetic XXZ chain and |vac>' is the vacuum eigenstate of an infinite-size XXZ chain which is split in two. We consider the quantity −log(f) which has been put forward as a measure of quantum entanglement, and show that the large correlation length ξ behaviour is consistent with a general conjecture −log(f) ~ c/8 log(ξ), where c is the central charge of the UV conformal field theory (with c = 1 for the XXZ chain). This behaviour is a natural extension of the existing conformal field theory prediction of −log(f) ~ c/8 log(L) for a length L bipartite system with 0 <L<ξ.
Zoltan Zimboras (Poster)
Title: Area law violation for the mutual information in a nonequilibrium steady state
Abstract: We study the nonequilibrium steady state of an infinite chain of free fermions, resulting from an initial state where the two sides of the system are prepared at different temperatures. The mutual information is calculated between two adjacent segments of the chain and is found to scale logarithmically in the subsystem size. This provides the first example of the violation of the area law in a quantum many-body system outside a zero temperature regime. The prefactor of the logarithm is obtained analytically and, furthermore, the same prefactor is shown to govern the logarithmic increase of mutual information in time, before the system relaxes locally to the steady state.
Published as V. Eisler and Z. Zimboras, Phys. Rev. A 89, 032321 (2014)