The Negativity Hamiltonian: An operator characterization of mixed-state entanglement

Abstract

In the context of ground states of quantum many-body systems, the locality of entanglement between connected regions of space is directly tied to the locality of the corresponding entanglement Hamiltonian: the latter is dominated by local, few-body terms. In this work, we introduce the negativity Hamiltonian as the (non hermitian) effective Hamiltonian operator describing the logarithm of the partial transpose of a many-body system. This allows us to address the connection between entanglement and operator locality beyond the paradigm of bipartite pure systems. As a first step in this direction, we study the structure of the negativity Hamiltonian for fermionic conformal field theories and a free fermion chain: in both cases, we show that the negativity Hamiltonian assumes a quasi-local functional form, that is captured by simple functional relations.

arXiv comment7 pages, 3 figures; Suppl. Mat.: 8 pages, 4 figures

References in corpus (95)

• Separability Criterion for Density Matrices
• A computable measure of entanglement
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• The density-matrix renormalization group in the age of matrix product states
• Peres-Horodecki separability criterion for continuous variable systems
• Entropy and Area
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• The logarithmic negativity: A full entanglement monotone that is not convex
• Towards a derivation of holographic entanglement entropy
• Cool horizons for entangled black holes
• Measuring entanglement entropy through the interference of quantum many-body twins
• Quantum thermalization through entanglement in an isolated many-body system
• Building up spacetime with quantum entanglement
• Calculation of reduced density matrices from correlation functions
• Quantum entanglement in condensed matter systems
• Reduced density matrices and entanglement entropy in free lattice models
• Probing entanglement entropy via randomized measurements
• Probing entanglement in a many-body-localized system
• Entanglement negativity in quantum field theory
• Entanglement Properties of the Harmonic Chain
• The Gravity Dual of Renyi Entropy
• Mixed-state entanglement from local randomized measurements
• Entanglement negativity in extended systems: A field theoretical approach
• Entanglement Temperature and Entanglement Entropy of Excited States
• Entanglement hamiltonians in two-dimensional conformal field theory
• Symmetry-resolved entanglement detection using partial transpose moments
• Parity effects in the scaling of block entanglement in gapless spin chains
• Finite temperature entanglement negativity in conformal field theory
• Reduced density matrix and internal dynamics for multicomponent regions
• Partial time-reversal transformation and entanglement negativity in fermionic systems
• Entanglement negativity in the harmonic chain out of equilibrium
• Analog quantum chemistry simulation
• Entanglement negativity after a global quantum quench
• Quantum Simulation and Spectroscopy of Entanglement Hamiltonians
• Entanglement Hamiltonian Tomography in Quantum Simulation
• Entanglement negativity and topological order
• Negativity and topological order in the toric code
• Critical and noncritical long range entanglement in the Klein-Gordon field
• On the partial transpose of fermionic Gaussian states
• The entanglement negativity in random spin chains
• Edge theory approach to topological entanglement entropy, mutual information and entanglement negativity in Chern-Simons theories
• Scaling of entanglement between separated blocks in spin chains at criticality
• Entanglement negativity in the critical Ising chain
• Entanglement negativity of fermions: monotonicity, separability criterion, and classification of few-mode states
• Entanglement negativity and entropy in non-equilibrium conformal field theory
• Many-body topological invariants for fermionic symmetry-protected topological phases
• Entanglement probe of two-impurity Kondo physics in a spin chain
• Entanglement negativity after a local quantum quench in conformal field theories
• Detecting Topological Order at Finite Temperature Using Entanglement Negativity
• Entropy and modular Hamiltonian for a free chiral scalar in two intervals
• Density Matrices for a Chain of Oscillators
• Entanglement negativity bounds for fermionic Gaussian states
• Local temperatures and local terms in modular Hamiltonians
• Twisted and untwisted negativity spectrum of free fermions
• Negativity spectrum of one-dimensional conformal field theories
• Quantum information dynamics in multipartite integrable systems
• Many-body topological invariants in fermionic symmetry protected topological phases: Cases of point group symmetries
• Entanglement Hamiltonians of lattice models via the Bisognano-Wichmann theorem
• Entanglement negativity in two-dimensional free lattice models
• Measuring Fermionic Entanglement: Entropy, Negativity, and Spin Structure
• Analytical results for the entanglement Hamiltonian of a free-fermion chain
• Entanglement Routers Using Macroscopic Singlets
• Nonzero temperature Entanglement Negativity of quantum spin models: Area law, Linked Cluster Expansions and Sudden Death
• Thermal bound entanglement in macroscopic systems and area laws
• Entanglement Hamiltonian of Interacting Fermionic Models
• Modular Groups of Quantum Fields in Thermal States
• Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories
• Topological entanglement negativity in Chern-Simons theories
• Properties of the entanglement Hamiltonian for finite free-fermion chains
• Quantum Variational Learning of the Entanglement Hamiltonian
• Singularity in Entanglement Negativity Across Finite Temperature Phase Transitions
• Entanglement negativity spectrum of random mixed states: A diagrammatic approach
• Entanglement hamiltonians in 1D free lattice models after a global quantum quench
• Branch Point Twist Field Correlators in the Massive Free Boson Theory
• Universal scaling of the logarithmic negativity in massive quantum field theory
• On entanglement hamiltonians of an interval in massless harmonic chains
• Entanglement negativity in a two dimensional harmonic lattice: Area law and corner contributions
• The entanglement spectrum of chiral fermions on the torus
• Entanglement structure of current-driven diffusive fermion systems
• Entanglement negativity and sudden death in the toric code at finite temperature
• Distillable entanglement and area laws in spin and harmonic-oscillator systems
• On the continuum limit of the entanglement Hamiltonian
• Reconstructing Entanglement Hamiltonian via Entanglement Eigenstates
• Geometric modular action for disjoint intervals and boundary conformal field theory
• Entanglement Hamiltonians for chiral fermions with zero modes
• Modular Hamiltonians for the massless Dirac field in the presence of a boundary
• Modular Hamiltonians for the massless Dirac field in the presence of a defect
• Entanglement Content of Quantum Particle Excitations I. Free Field Theory
• Negativity spectrum in 1D gapped phases of matter
• Negativity Spectrum in the Random Singlet Phase
• Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains
• The negativity contour: a quasi-local measure of entanglement for mixed states
• Measuring von Neumann entanglement entropies without wave functions
• Entanglement and classical fluctuations at finite-temperature critical points
• Entanglement Content of Quantum Particle Excitations III. Graph Partition Functions

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• Finite Temperature Entanglement Negativity of Fermionic Symmetry Protected Topological Phases and Quantum Critical Points in One Dimension
• Quasiparticle Picture for Entanglement Hamiltonians in Higher Dimensions
• Symmetry resolution of the computable cross-norm negativity of two disjoint intervals in the massless Dirac field theory
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• Breakdown of Measurement-Induced Phase Transitions Under Information Loss
• Ansatz-free Hamiltonian learning with Heisenberg-limited scaling
• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• Quench dynamics of negativity Hamiltonians
• Fermionic Partial Transpose in the Overlap Matrix Framework for Entanglement Negativity
• Dynamics of charge-imbalance-resolved entanglement negativity after a quench in a free-fermion model
• A contour for the entanglement negativity of bosonic Gaussian states
• Entanglement Hamiltonian during a domain wall melting in the free Fermi chain
• Entanglement Spectroscopy and probing the Li-Haldane Conjecture in Topological Quantum Matter