Deviation from maximal entanglement for mid-spectrum eigenstates of local Hamiltonians
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.
Keywords
Cite
@article{arxiv.2202.01173,
title = {Deviation from maximal entanglement for mid-spectrum eigenstates of local Hamiltonians},
author = {Yichen Huang},
journal= {arXiv preprint arXiv:2202.01173},
year = {2024}
}
Comments
v2: major revision with significantly improved results and presentation; v3: published version