## Entanglement of exact excited eigenstates of the Hubbard model in arbitrary dimension

Oskar Vafek, Nicolas Regnault, B. Andrei Bernevig

SciPost Phys. 3, 043 (2017) · published 26 December 2017

- doi: 10.21468/SciPostPhys.3.6.043
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### 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.

### Cited by 11

### Ontology / Topics

See full Ontology or Topics database.### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1 }^{2 }^{3 }Oskar Vafek, -
^{2 }^{4 }^{5 }Nicolas Regnault, -
^{2 }Bogdan Andrei Bernevig

^{1}National High Magnetic Field Laboratory [MagLab]^{2}Princeton University^{3}Florida State University [FSU]^{4}École Normale Supérieure [ENS]^{5}Sorbonne Universités / Sorbonne University

- Army Research Office (ARO) (through Organization: United States Army Research Laboratory [ARL])
- David and Lucile Packard Foundation
- National Science Foundation [NSF]
- Office of Naval Research [ONR]
- Simons Foundation
- U.S. Department of Defense (DOD) (through Organization: United States Department of Defense [DOD])
- United States Department of Energy [DOE]