Entanglement in solvable many-particle models

Abstract

Lecture notes for the Brazilian School on Statistical Mechanics, Natal, Brazil, July 2011. The five lectures introduce to the description of entanglement in many-particle systems and review the ground-state entanglement features of standard solvable lattice models. This is done using a thermodynamic formulation in which the eigenvalue spectrum of a certain Hamiltonian determines the entanglement properties. The methods to obtain it are discussed and results, both analytical and numerical, for various cases including time evolution are presented.

44 pages, 30 figures. Lecture notes for the Brazilian School on Statistical Mechanics, Natal, July 2011. For the Brazilian Journal of Physics

References in corpus (11)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Quantum Noise as an Entanglement Meter
• The entanglement entropy of one-dimensional gases
• Entanglement evolution after connecting finite to infinite quantum chains
• Solution of the fermionic entanglement problem with interface defects
• Entanglement in spin chains with gradients
• On the relation between entanglement and subsystem Hamiltonians
• Essential singularity in the Renyi entanglement entropy of the one-dimensional XYZ spin-1/2 chain
• Corrections to scaling for block entanglement in massive spin-chains

Cited by in corpus (116)

• Quantum entanglement in condensed matter systems
• Density matrix embedding: A simple alternative to dynamical mean-field theory
• Density matrix embedding: A strong-coupling quantum embedding theory
• Kitaev chains with long-range pairing
• Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory
• Long-range Ising and Kitaev Models: Phases, Correlations and Edge Modes
• Symmetry resolved entanglement in free fermionic systems
• Density Matrix Embedding from Broken Symmetry Lattice Mean-Fields
• Exactly-embedded multiconfigurational self-consistent field theory using density matrix embedding: the localized active space self-consistent field method
• Rényi generalization of the operational entanglement entropy
• Quench dynamics of a Tonks-Girardeau gas released from a harmonic trap
• Quantum quench from a thermal tensor state: boundary effects and generalized Gibbs ensemble
• The quantum Ising chain for beginners
• Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach
• Scaling of Rényi entanglement entropies of the free Fermi-gas ground state: a rigorous proof
• Random matrices and entanglement entropy of trapped Fermi gases
• Can Density Matrix Embedding Theory with the Complete Activate Space Self-Consistent Field Solver Describe Single and Double Bond Breaking in Molecular Systems?
• Negativity spectrum of one-dimensional conformal field theories
• Long-range topological insulators and weakened bulk-boundary correspondence
• Random free fermions: An analytical example of eigenstate thermalization
• Symmetry resolved entanglement in two-dimensional systems via dimensional reduction
• Entanglement spreading in non-equilibrium integrable systems
• Analytical results for the entanglement Hamiltonian of a free-fermion chain
• The Variational Localized Active Space Self-Consistent Field Method
• Boundary effects on symmetry resolved entanglement
• Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model
• Real time evolution of Anderson impurity models via tensor network influence functionals
• Effective Theory and Breakdown of Conformal Symmetry in a Long-Range Quantum Chain
• Entanglement revivals as a probe of scrambling in finite quantum systems
• Subsystem Trace Distance in Quantum Field Theory
• Ground-state phase diagram of the three-band Hubbard model from density matrix embedding theory
• Explicit Hamiltonians Inducing Volume Law for Entanglement Entropy in Fermionic Lattices
• Landauer-Büttiker approach to strongly coupled quantum thermodynamics: inside-outside duality of entropy evolution
• A path integral Monte Carlo method for Rényi entanglement entropies
• Left-Right Entanglement Entropy of Boundary States
• Efficient variational approach to the impurity problem and its application to the dynamical mean-field theory
• Equipartition of Entanglement in Quantum Hall States
• Finite and Infinite Matrix Product States for Gutzwiller Projected Mean-Field Wavefunctions
• Interplay of disorder and interactions in a flat-band supporting diamond chain
• Black holes as random particles: entanglement dynamics in infinite range and matrix models
• Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion
• Entanglement contour perspective for strong area law violation in a disordered long-range hopping model
• Exact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model
• Subsystem trace distance in low-lying states of $(1+1)$-dimensional conformal field theories
• Theory of Non-Interacting Fermions and Bosons in the Canonical Ensemble
• Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains
• Entanglement evolution across defects in critical anisotropic Heisenberg chains
• Landauer Current and Mutual Information
• Study of counterintuitive transport properties in the Aubry-André-Harper model via entanglement entropy and persistent current
• Exact hydrodynamic description of symmetry-resolved Rényi entropies after a quantum quench
• Divergence of entanglement entropy in quantum systems: Zero-modes
• Edge insulating topological phases in a two-dimensional long-range superconductor
• Many-body entanglement in a topological chiral ladder
• Incremental Embedding: A Density Matrix Embedding Scheme for Molecules
• Corrections to universal Rényi entropy in quasiparticle excited states of quantum chains
• Family-Vicsek dynamical scaling and Kardar-Parisi-Zhang-like superdiffusive growth of surface roughness in a driven one-dimensional quasiperiodic model
• Entanglement of magnon excitations in spin chains
• Universal signatures of Dirac fermions in entanglement and charge fluctuations
• Dealing with the exponential wall in electronic structure calculations
• Entanglement and negativity Hamiltonians for the massless Dirac field on the half line
• Direct calculation of the Entanglement Spectrum in Quantum Monte Carlo with application to \textit{ab initio} Hamiltonians
• Compound-tunable embedding potential method and its application to fersmite crystal
• Unbiasing Fermionic Auxiliary-Field Quantum Monte Carlo with Matrix Product State Trial Wavefunctions
• Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory -- I. Single-particle states
• Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part II. Multi-particle states
• Entanglement Entropy of the Low-Lying Excited States and Critical Properties of an Exactly Solvable Two-Leg Spin Ladder with Three-Spin Interactions
• Flat bands and entanglement in the Kitaev ladder
• One-to-one correspondence between entanglement mechanics and black hole thermodynamics
• Scaling of fronts and entanglement spreading during a domain wall melting
• Entanglement measures and non-equilibrium dynamics of quantum many-body systems: a path integral approach
• Tensor network influence functionals in the continuous-time limit: connections to quantum embedding, bath discretization, and higher-order time propagation
• On the Mutual Information in Conformal Field Theory
• Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model
• Entanglement of Free Fermions on Johnson Graphs
• Entanglement entropy and entanglement spectrum of triplet topological superconductors
• Entanglement Hamiltonians and the quasiparticle picture
• Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices
• Subsystem distances between quasiparticle excited states
• Mutual information for fermionic systems
• Entanglement of Free Fermions on Hadamard Graphs
• Entanglement spectrum as a marker for phase transitions in the density embedding theory for interacting spinless fermionic models
• The scaling of entanglement entropy in a honeycomb lattice on a torus
• Comparative study of the density matrix embedding theory for the Hubbard models
• Finite temperature negativity Hamiltonians of the massless Dirac fermion
• Non-stochastic matrix Schrödinger equation for open systems
• Evidence of quantum phase transition in real-space vacuum entanglement of higher derivative scalar quantum field theories
• The dynamical $\alpha$-Rényi entropies of local Hamiltonians grow at most linearly in time
• Holographic encoding of universality in corner spectra
• Simple embedding scheme for the spectral properties of the Single-Impurity Anderson Model
• Quantum entanglement and transport in non-equilibrium interacting double-dot setup: The curious role of degeneracy
• Geometry and Dynamics of Emergent Spacetime from Entanglement Spectrum
• Landauer current and mutual information in a bosonic quantum dot
• Geometric Entanglement and Quantum Phase Transition in Generalized Cluster-XY models
• Gutzwiller Renormalization Group
• Production of Entanglement Entropy by Decoherence
• Block entanglement and fluctuations in finite size correlated electron systems
• Entanglement entropy of random partitioning
• Effect of Single Impurity on Free Fermion Entanglement Entropy
• Density matrix of electrons coupled to phonons and the electron-phonon entanglement content of excited states
• Bulk-entanglement spectrum correspondence in $PT$- and $PC$-symmetric topological insulators and superconductors
• Slow relaxation and sensitivity to disorder in trapped lattice fermions after a quench
• Constructive Fermionic Matrix Product States for Projected Fermi Sea
• Entanglement of electrons and the lattice in a Luttinger system
• Optimizing Electronic Structure Simulations on a Trapped-ion Quantum Computer using Problem Decomposition
• A hydrodynamic approach to Stark localization
• Effective thermodynamics of isolated entangled squeezed and coherent states
• Rainbow chains and numerical renormalisation group for accurate chiral conformal spectra
• Coupling modifies the quantum fluctuations of entangled oscillators
• Entanglement entropy in multi-leg Kitaev ladders with interface defects
• Bound energy, entanglement and identifying critical points in 1D long-range Kitaev model
• Long term behavior of the stirred vacuum on a Dirac chain: geometry blur and the random Slater ensemble
• Entanglement dynamics of a hard-core quantum gas during a Joule expansion
• On Emergent Geometry from Entanglement Entropy in Matrix theory
• Emergent geometry through quantum entanglement in Matrix theories
• Entanglement entropy as a probe of topological phase transitions
• Entanglement Hamiltonian during a domain wall melting in the free Fermi chain