TY - JOUR

T1 - Conserved quantities from entanglement Hamiltonian

AU - Lian, Biao

N1 - Funding Information:
The author is grateful to conversations with Yichen Hu, Abhinav Prem, and especially the insightful discussion with David Huse. The author is also thankful to the comments from the referees which helps improve this paper. The author acknowledges support from the Alfred P. Sloan Foundation.
Publisher Copyright:
©2022 American Physical Society

PY - 2022/1/15

Y1 - 2022/1/15

N2 - 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 O(subregionboundaryareasubregionvolume). By diagonalizing an entanglement Hamiltonian superdensity matrix (EHSM) for an ensemble of eigenstates, we can obtain these conserved quantities as the EHSM eigenoperators 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 eigenoperators can be rather nonlocal, although subregionally quasilocal. In the interacting XYZ model, we numerically find the nonzero EHSM eigenvalues decay roughly as a power law if the system is integrable, with the exponent s≈1 (s≈1.5–2) if the eigenstates are extended (many-body localized). For fully chaotic systems, only two EHSM eigenvalues are significantly nonzero, the eigenoperators of which correspond to the identity and the subregion Hamiltonian.

AB - 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 O(subregionboundaryareasubregionvolume). By diagonalizing an entanglement Hamiltonian superdensity matrix (EHSM) for an ensemble of eigenstates, we can obtain these conserved quantities as the EHSM eigenoperators 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 eigenoperators can be rather nonlocal, although subregionally quasilocal. In the interacting XYZ model, we numerically find the nonzero EHSM eigenvalues decay roughly as a power law if the system is integrable, with the exponent s≈1 (s≈1.5–2) if the eigenstates are extended (many-body localized). For fully chaotic systems, only two EHSM eigenvalues are significantly nonzero, the eigenoperators of which correspond to the identity and the subregion Hamiltonian.

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U2 - 10.1103/PhysRevB.105.035106

DO - 10.1103/PhysRevB.105.035106

M3 - Article

AN - SCOPUS:85122473049

SN - 2469-9950

VL - 105

JO - Physical Review B

JF - Physical Review B

IS - 3

M1 - 035106

ER -