Entanglement of Exact Excited Eigenstates of the Hubbard Model in Arbitrary Dimension

TL;DR

This paper calculates the entanglement entropy of exact excited eigenstates in the Hubbard model, revealing diverse scaling behaviors and violations of strong ETH, offering insights into thermalization dynamics in quantum many-body systems.

Contribution

It provides exact entanglement entropy calculations for eta-pairing states in the Hubbard model across arbitrary dimensions, highlighting novel scaling laws and ETH violations.

Findings

Entanglement entropy scales logarithmically with system size for singlet eta-pairing states.

Finite spin magnetization states show volume or area-times-log scaling depending on fermion occupation.

States violate strong ETH, useful for studying thermalization processes.

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 Renyi 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.