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Universal eigenstate entanglement of chaotic local Hamiltonians
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This arXiv repository is a bundle of two closely related papers. Abstract of the first paper: In systems governed by "chaotic" local Hamiltonians, we conjecture the universality of eigenstate entanglement (defined as the average entanglement entropy of all eigenstates) by proposing an exact formula for its dependence on the subsystem size. This formula is derived from an analytical argument based on a plausible assumption, and is supported by numerical simulations. Abstract of the second paper: In systems governed by chaotic local Hamiltonians, the first paper conjectured the universality of the average entanglement entropy of all eigenstates by proposing an exact formula for its dependence on the subsystem size. In this note, I extend this result to the average entanglement entropy of a constant fraction of eigenstates in the middle of the energy spectrum. The generalized formula is supported by numerical simulations of various chaotic spin chains.
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Extreme value statistics and eigenstate thermalization in kicked quantum chaotic spin-$1/2$ chains
The largest entanglement eigenvalue of a quantum chaotic kicked Ising chain follows a Weibull-type extreme value distribution rather than the random-matrix Tracy-Widom law, even as ETH is satisfied.
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