arXiv:2202.01173 · IEEE Journal on Selected Areas in Information Theory

Deviation From Maximal Entanglement for Mid-Spectrum Eigenstates of Local Hamiltonians

Yichen Huang

Published Jan 1, 2024• 1 citation

Abstract

In a spin chain governed by a local Hamiltonian, we consider a microcanonical ensemble in the middle of the energy spectrum and a contiguous subsystem whose length is a constant fraction of the system size. We prove that if the bandwidth of the ensemble is greater than a certain constant, then the average entanglement entropy (between the subsystem and the rest of the system) of eigenstates in the ensemble deviates from the maximum entropy by at least a positive constant. This result highlights the difference between the entanglement entropy of mid-spectrum eigenstates of (chaotic) local Hamiltonians and that of random states. We also prove that the former deviates from the thermodynamic entropy at the same energy by at least a positive constant.

DOI: 10.1109/jsait.2024.3487856

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