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Volume Law and Quantum Criticality in the Entanglement Entropy of Excited Eigenstates of the Quantum Ising Model
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Much has been learned about universal properties of entanglement entropies in ground states of quantum many-body lattice systems. Here we unveil universal properties of the average bipartite entanglement entropy of eigenstates of the paradigmatic quantum Ising model in one dimension. The leading term exhibits a volume-law scaling that we argue is universal for translationally invariant quadratic models. The subleading term is constant at the critical field for the quantum phase transition and vanishes otherwise (in the thermodynamic limit), i.e., the critical field can be identified from subleading corrections to the average (over all eigenstates) entanglement entropy.
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Efficient computation of average subsystem Bures distance between fermionic Gaussian states
An efficient Bures-distance algorithm for fermionic Gaussian states shows linear average subsystem-distance growth in the integrable Ising chain, but not in quadratic SYK or random Gaussian states.
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