Abstract
We compute exactly the von Neumann entanglement entropy of the eta-pairing states - a large set of exact excited eigenstates of the Hubbard Hamiltonian. For the singlet eta-pairing states the entropy scales with the logarithm of the spatial dimension of the (smaller) partition. For the eta-pairing states with finite spin magnetization density, the leading term can scale as the volume or as the area-times-log, depending on the momentum space occupation of the Fermions with flipped spins. We also compute the corrections to the leading scaling. In order to study the eigenstate thermalization hypothesis (ETH), we also compute the entanglement Rényi entropies of such states and compare them with the corresponding entropies of thermal density matrix in various ensembles. Such states, which we find violate strong ETH, may provide a useful platform for a detailed study of the time-dependence of the onset of thermalization due to perturbations which violate the total pseudospin conservation.
Highlights
D.2 On why there must be a single peak in {mA} α2{mA} as a function NA
The question of how equilibration and thermalization arise in isolated quantum systems led to the eigenstate thermalization hypothesis (ETH) [1,2,3,4]
We find that even for the states with volume law entanglement, the entanglement Rényi entropies do not match those of the thermal density matrix in the canonical ensemble
Summary
The question of how equilibration and thermalization arise in isolated quantum (many-body) systems led to the eigenstate thermalization hypothesis (ETH) [1,2,3,4]. The entanglement entropy for these states shows either a ln(V ) law, or a V (volume) law, or even an area-times-log law, depending on the number and the momentum space distribution of the flipped spins in the state. When their entropy is sub-extensive, such states clearly violate strong ETH. Despite being in the middle of the full Hubbard spectrum, the pure spin singlet eta-pairing states, which show ln(V ) entanglement, are simultaneously the ground-states and the most excited states in their specific quantum number sectors. The eta-pairing states with flipped spins are richer They display either volume or area-times-log entanglement, depending on the momentum space occupation of the flipped Fermions. They match the Rényi entropy of the thermal density matrix in a grand canonical ensemble, but with additional constraints on the quantum numbers of the states
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