Entanglement of exact excited eigenstates of the Hubbard model in arbitrary dimension
Abstract
We compute exactly the von Neumann entanglement entropy of the etapairing states  a large set of exact excited eigenstates of the Hubbard Hamiltonian. For the singlet etapairing states the entropy scales with the logarithm of the spatial dimension of the (smaller) partition. For the etapairing states with finite spin magnetization density, the leading term can scale as the volume or as the areatimeslog, 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 timedependence of the onset of thermalization due to perturbations which violate the total pseudospin conservation.
 Authors:

 Florida State University, National High Magnetic Field Laboratory, Princeton University
 Sorbonne University, École Normale Supérieure, Princeton University
 Princeton University
 Publication Date:
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1414843
 Grant/Contract Number:
 SC0016239
 Resource Type:
 Published Article
 Journal Name:
 SciPost Physics Proceedings
 Additional Journal Information:
 Journal Name: SciPost Physics Proceedings Journal Volume: 3 Journal Issue: 6; Journal ID: ISSN 25424653
 Publisher:
 Stichting SciPost
 Country of Publication:
 Netherlands
 Language:
 English
Citation Formats
Vafek, Oskar, Regnault, Nicolas, and Bernevig, B. Andrei. Entanglement of exact excited eigenstates of the Hubbard model in arbitrary dimension. Netherlands: N. p., 2017.
Web. https://doi.org/10.21468/SciPostPhys.3.6.043.
Vafek, Oskar, Regnault, Nicolas, & Bernevig, B. Andrei. Entanglement of exact excited eigenstates of the Hubbard model in arbitrary dimension. Netherlands. https://doi.org/10.21468/SciPostPhys.3.6.043
Vafek, Oskar, Regnault, Nicolas, and Bernevig, B. Andrei. Tue .
"Entanglement of exact excited eigenstates of the Hubbard model in arbitrary dimension". Netherlands. https://doi.org/10.21468/SciPostPhys.3.6.043.
@article{osti_1414843,
title = {Entanglement of exact excited eigenstates of the Hubbard model in arbitrary dimension},
author = {Vafek, Oskar and Regnault, Nicolas and Bernevig, B. Andrei},
abstractNote = {We compute exactly the von Neumann entanglement entropy of the etapairing states  a large set of exact excited eigenstates of the Hubbard Hamiltonian. For the singlet etapairing states the entropy scales with the logarithm of the spatial dimension of the (smaller) partition. For the etapairing states with finite spin magnetization density, the leading term can scale as the volume or as the areatimeslog, 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 timedependence of the onset of thermalization due to perturbations which violate the total pseudospin conservation.},
doi = {10.21468/SciPostPhys.3.6.043},
journal = {SciPost Physics Proceedings},
number = 6,
volume = 3,
place = {Netherlands},
year = {2017},
month = {12}
}
https://doi.org/10.21468/SciPostPhys.3.6.043
Web of Science
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