Conserved Quantities from Entanglement Hamiltonian
arXiv:2104.11753 · doi:10.1103/PhysRevB.105.035106
Abstract
We show that the subregion entanglement Hamiltonians of excited eigenstates of a quantum many-body system are approximately linear combinations of subregionally (quasi)local approximate conserved quantities, with relative commutation errors . By diagonalizing an entanglement Hamiltonian superdensity matrix (EHSM) for an ensemble of eigenstates, we can obtain these conserved quantities as the EHSM eigen-operators with nonzero eigenvalues. For free fermions, we find the number of nonzero EHSM eigenvalues is cut off around the order of subregion volume, and some of their EHSM eigen-operators can be rather nonlocal, although subregionally quasilocal. In the interacting XYZ model, we numerically find the nonzero EHSM eigenvalues decay roughly in power law if the system is integrable, with the exponent () if the eigenstates are extended (many-body localized). For fully chaotic systems, only two EHSM eigenvalues are significantly nonzero, the eigen-operators of which correspond to the identity and the subregion Hamiltonian.
arXiv comment7+23 pages, 6+9 figures, extended to a long article
References in corpus (39)
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- A bound on chaos
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
- Localization of interacting fermions at high temperature
- Comments on the Sachdev-Ye-Kitaev model
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- The many-body localization phase transition
- Calculation of reduced density matrices from correlation functions
- Many body localization in Heisenberg XXZ magnet in a random field
- Interacting electrons in disordered wires: Anderson localization and low-temperature transport
- Phenomenology of fully many-body-localized systems
- A phenomenology of certain many-body-localized systems
- Local conservation laws and the structure of the many-body localized states
- The Spectrum in the Sachdev-Ye-Kitaev Model
- Generalized Gibbs ensemble in integrable lattice models
- Time evolution of local observables after quenching to an integrable model
- The approach to thermal equilibrium in quantized chaotic systems
- Integrals of motion in the Many-Body localized phase
- The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
- Generalized Thermalization in an Integrable Lattice System
- Constructing local integrals of motion in the many-body localized phase
- Constructing the generalized Gibbs ensemble after a quantum quench
- Does a single eigenstate encode the full Hamiltonian?
- Quasilocal conserved operators in isotropic Heisenberg spin 1/2 chain
- Structure of the conservation laws in integrable spin chains with short range interactions
- Determining a local Hamiltonian from a single eigenstate
- Bounds on chaos from the eigenstate thermalization hypothesis
- Renyi Entropy of Chaotic Eigenstates
- Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems
- Structure of chaotic eigenstates and their entanglement entropy
- Generalized Eigenstate Thermalization in 2d CFTs
- Proof of the absence of local conserved quantities in the XYZ chain with a magnetic field
- Explicit Construction of Local Conserved Quantities in the XYZ Spin-1/2 Chain
- The chiral SYK model
- Breakdown of quantum-classical correspondence and dynamical generation of entanglement