Reduced density matrices and entanglement entropy in free lattice models

Abstract

We review the properties of reduced density matrices for free fermionic or bosonic many-particle systems in their ground state. Their basic feature is that they have a thermal form and thus lead to a quasi-thermodynamic problem with a certain free-particle Hamiltonian. We discuss the derivation of this result, the character of the Hamiltonian and its eigenstates, the single-particle spectra and the full spectra, the resulting entanglement and in particular the entanglement entropy. This is done for various one- and two-dimensional situations, including also the evolution after global or local quenches.

33 pages, 18 figures, minor changes, references added. Review article for the special issue "Entanglement entropy in extended systems" in J. Phys. A

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• Exact relationship between the entanglement entropies of XY and quantum Ising chains
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• Floquet engineered inhomogeneous quantum chaos in critical systems
• Entangelment Entropy on Generalized Brillouin Zone
• Generalized thermalization for integrable system under quantum quench
• Simple embedding scheme for the spectral properties of the Single-Impurity Anderson Model
• Zero-mode entanglement across a conformal defect
• Boundary Symmetry Breaking in CFT and the String Order Parameter
• Investigation of the Quantum Correlations for a S=1/2 Ising- Heisenberg Model on a Symmetrical Diamond Chain
• Entanglement in non-critical inhomogeneous quantum chains
• Topologically distinct critical theories emerging from the bulk entanglement spectrum of integer quantum Hall states on a lattice
• Entanglement Measures in a Nonequilibrium Steady State: Exact Results in One Dimension
• Quench dynamics of Rényi negativities and the quasiparticle picture
• On the Bisognano-Wichmann entanglement Hamiltonian of nonrelativistic fermions
• Efficient and quantum-adaptive machine learning with fermion neural networks
• Entanglement gap, corners, and symmetry breaking
• Finite entanglement properties in the matrix product states of the one-dimensional Hubbard model
• Fermionic tensor networks for higher order topological insulators from charge pumping
• Construction of interacting flat-band models by molecular-orbital representation: Correlation functions, energy gap, and entanglement
• Mesoscopic fluctuations in entanglement dynamics
• Schmidt gap in random spin chains
• Free fermions with dephasing and boundary driving: Bethe Ansatz results
• Entanglement Hamiltonian of Interacting Systems: Local Temperature Approximation and Beyond
• Detection of Topology via Entanglement Oscillations
• Structure of the Hamiltonian of mean force
• On Landauer--Büttiker formalism from a quantum quench
• Quantifying fermionic interactions from the violation of Wick's theorem
• Reentrant topological phases and entanglement scalings in moiré-modulated extended Su-Schrieffer-Heeger Model
• Controlling measurement-induced phase transitions with tunable detector coupling
• Healing of Defects in Random Antiferromagnetic Spin Chains
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices
• Production of Entanglement Entropy by Decoherence
• Bulk Reconstruction from Generalized Free Fields
• Entanglement Dynamics between Ising Spins and a Central Ancilla
• Single-quasiparticle eigenstate thermalization
• Clustering of conditional mutual information and quantum Markov structure at arbitrary temperatures
• Entanglement transition through Hilbert-space localization
• Fermionic logarithmic negativity in the Krawtchouk chain
• Correlations at higher-order exceptional points in non-Hermitian models
• Analytic Expression for the Entanglement Entropy of a 2D Topological Superconductor
• Entanglement phase transitions in non-Hermitian Kitaev chains
• Quantum feedback induced entanglement relaxation and dynamical phase transition in monitored free fermion chains with Wannier-Stark ladder
• Symmetry classification of typical quantum entanglement
• Area laws and thermalization from classical entropies in a Bose-Einstein condensate
• Entanglement after Quantum Quenches in Lifshitz Scalar Theories
• A finite temperature study of ideal quantum gases in the presence of one dimensional quasi-periodic potential
• Tracking locality in time evolution of disordered systems
• Breakdown of local convertibility through Majorana modes in a quantum quench
• Nonlocal fermions and the entropy volume law
• Accuracy of time-dependent GGE under weak dissipation
• Entanglement in Lifshitz Fermion Theories
• Deep learning of topological phase transitions from entanglement aspects for two-dimensional chiral p-wave superconductors
• Page Curve and Entanglement Dynamics in an Interacting Fermionic Chain
• Boiling Quantum Vacuum: Thermal Subsystems from Ground-State Entanglement
• Entanglement of Free Fermions and Bosons at Finite Temperature
• Reduced fidelities for free fermions out of equilibrium: From dynamical quantum phase transitions to Mpemba effect
• Entanglement entropy for the valence bond solid phases of two-dimensional dimerized Heisenberg antiferromagnets
• Breakdown of quantum-classical correspondence and dynamical generation of entanglement
• Exact quench dynamics of symmetry resolved entanglement in a free fermion chain
• Emergent eigenstate solution for generalized thermalization
• Quantum Correlations in Field Theory and Integrable Systems
• $\mathcal{P}\mathcal{T}$-symmetry phase transition in a Bose-Hubbard model with localized gain and loss
• Energy bounds for entangled states
• Dynamics of logarithmic negativity and mutual information in smooth quenches
• Universality in the tripartite information after global quenches: spin flip and semilocal charges
• Area law and universality in the statistics of subsystem energy
• Entropy estimation in a spin-1 Bose-Einstein condensate
• Relaxation of the entanglement spectrum in quench dynamics of topological systems
• Measurement-induced phase transition in periodically driven free-fermionic systems
• Entanglement-fluctuation relation for bipartite pure states
• Renyi information from entropic effects in one higher dimension
• Dynamics of entanglement fluctuations and quantum Mpemba effect in the $\nu =1$ QSSEP model
• Quantum geometry and geometric entanglement entropy of one-dimensional Floquet topological matter
• Entanglement entropy of dispersive media from thermodynamic entropy in one higher dimension
• Boundary-law scaling of entanglement entropy in diffusive metals
• Quantum Generalized Hydrodynamics of the Tonks-Girardeau gas: density fluctuations and entanglement entropy
• Building Entanglement Entropy out of Correlation Functions for Interacting Fermions
• Stacked tree construction for free-fermion projected entangled pair states
• Study of quantum non-locality by CHSH function and its extension in disordered fermions
• Entanglement of bosonic systems under monitored evolution
• Unusual Corrections to the Scaling of the Entanglement Entropy of the Excited states in Conformal Field Theory
• Quantum Liang Information Flow Probe of Causality across Critical Points
• Scaling of finite size effect of $\alpha$-Rényi entropy in disjointed intervals under dilation
• Interaction-driven phase transition in one dimensional mirror-symmetry protected topological insulator
• Directional scrambling of quantum information in helical multiferroics
• Entanglement entropy due to near horizon degrees of freedom
• Quench dynamics of negativity Hamiltonians
• $\nu$-QSSEP: A toy model for entanglement spreading in stochastic diffusive quantum systems
• Projective approach to the entanglement entropy of 1-$d$ fermions
• Nonlinear entanglement growth in inhomogeneous spacetimes
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• Quench-Probe Setup as Analyzer of Fractionalized Entanglement Spreading
• Entanglement Entropy of $(2+1)$D Quantum Critical Points with Quenched Disorder: Dimensional Reduction Approach
• Entanglement entropy in low-energy field theories at finite chemical potential
• Entanglement in the Quantum Spherical Model -- a Review
• A hydrodynamic approach to Stark localization
• Thermal Corrections to Rényi entropies for Free Fermions
• Entanglement manifestation of knot topology in a non-Hermitian lattice
• Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions
• Entanglement entropy in multi-leg Kitaev ladders with interface defects
• Quadratic Hamiltonian approach to heat transport in fermionic systems
• Simulating dynamics of the two-dimensional transverse-field Ising model: a comparative study of large-scale classical numerics
• Emergent gapless spiral phases and conformal Lifshitz criticality in the cluster Ising model with off-diagonal interactions
• Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials
• Fate of entanglement in quadratic Markovian dissipative systems
• (2+1)D topological phases with RT symmetry: many-body invariant, classification, and higher order edge modes
• Entanglement spreading after local and extended excitations in a free-fermion chain
• Observable-enriched entanglement
• Entanglement entropy of two disjoint intervals and spin structures in interacting chains in and out of equilibrium
• Extended edge modes and disorder preservation of a symmetry-protected topological phase out of equilibrium
• Machine Learning Entanglement Freedom Or: How I Learned to Stop Worrying and Love Linear Regression
• Towards Entanglement Entropy of Random Large-N Theories
• Entanglement gap in 1D long-range quantum spherical models
• Thermal Correction to Entanglement Spectrum for Conformal Field Theories
• Entanglement entropies of an interval in the free Schrödinger field theory on the half line
• Nonlocality of Observables in Quasi-Hermitian Quantum Theory
• Gaussian matrix product states cannot efficiently describe critical systems
• Dynamics of charge-imbalance-resolved entanglement negativity after a quench in a free-fermion model
• Emergence of Gaussianity in the thermodynamic limit of interacting fermions
• Entanglement entropies of an interval in the free Schrödinger field theory at finite density
• Measurement-Induced Entanglement in Conformal Field Theory
• Reentrant topology and reverse pumping in a quasiperiodic flux ladder
• Entanglement Hamiltonian during a domain wall melting in the free Fermi chain
• Construction and universal application of entanglement erasing partner states
• Layer-number parity induced topological phase transition
• Entanglement entropy as a probe of topological phase transitions
• Symmetry-protected topological wire in a topological vacuum
• Inhomogeneous quenches and GHD in the $\nu =1$ QSSEP model
• Entanglement spectrum of gapless topological phases: a case study with topological superconductors
• Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors
• Equivalence of Stabilizer and Shannon Rényi Entropies: Exact Results for Quantum Critical Chains
• Phase transitions from Heating to non-heating in SU(1, 1) quantum dynamics: applications to Bose-Einstein condensates and periodically driven coupled oscillators
• Volume-law entanglement entropy of typical pure quantum states
• Universal entanglement correction induced by relevant deformations at the quantum critical point
• Geometric additivity of modular commutator for multipartite entanglement
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems
• Localization transitions in quadratic systems without quantum chaos
• Vortex lattices in binary Bose-Einstein condensates: Collective modes, quantum fluctuations, and intercomponent entanglement
• Entanglement signatures of a percolating quantum system
• Entanglement Entropy of Free Fermions with a Random Matrix as a One-Body Hamiltonian
• Entanglement dynamics of a hard-core quantum gas during a Joule expansion
• Replica Keldysh field theory of quantum-jump processes: General formalism and application to imbalanced and inefficient fermion counting
• Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study
• Phase Space Entanglement Spectrum
• From Bell Products to Greenberger-Horne-Zeilinger states: Quantum Memories via emergent Hamiltonians
• On Emergent Geometry from Entanglement Entropy in Matrix theory
• Topological states of generalized dissipative Majorana wires
• A contour for the entanglement negativity of bosonic Gaussian states