Conserved Quantities from Entanglement Hamiltonian

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 $\mathcal{O}\left(\frac{\text{subregion boundary area}}{\text{subregion volume}}\right)$. 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 $s\approx 1$ ($s\approx 1.5\sim 2$) 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.

7+23 pages, 6+9 figures, extended to a long article

References in corpus (10)

• Thermalization and its mechanism for generic isolated quantum systems
• Localization of interacting fermions at high temperature
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• Integrals of motion in the Many-Body localized phase
• Generalized Thermalization in an Integrable Lattice System
• Constructing local integrals of motion in the many-body localized phase
• Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems
• Breakdown of quantum-classical correspondence and dynamical generation of entanglement

Cited by in corpus (2)

• Entanglement Entropy of Free Fermions in Timelike Slices
• A Quantum Breakdown Model: from Many-body Localization to Chaos with Scars