skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Entanglement of exact excited eigenstates of the Hubbard model in arbitrary dimension

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.

Authors:
 [1];  [2];  [3]
  1. Florida State University, National High Magnetic Field Laboratory, Princeton University
  2. Sorbonne University, École Normale Supérieure, Princeton University
  3. 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 2542-4653
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. doi: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. doi: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. doi: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 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.},
doi = {10.21468/SciPostPhys.3.6.043},
journal = {SciPost Physics Proceedings},
number = 6,
volume = 3,
place = {Netherlands},
year = {2017},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.21468/SciPostPhys.3.6.043

Citation Metrics:
Cited by: 6 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Entanglement in Quantum Critical Phenomena
journal, June 2003


η Condensate of Fermionic Atom Pairs via Adiabatic State Preparation
journal, June 2010


Thermalization and its mechanism for generic isolated quantum systems
journal, April 2008

  • Rigol, Marcos; Dunjko, Vanja; Olshanii, Maxim
  • Nature, Vol. 452, Issue 7189
  • DOI: 10.1038/nature06838

η pairing and off-diagonal long-range order in a Hubbard model
journal, November 1989


Two-dimensional Hubbard model: Numerical simulation study
journal, April 1985


High-temperature macroscopic entanglement
journal, January 2004


Pseudospin symmetry and new collective modes of the Hubbard model
journal, July 1990


Calculation of reduced density matrices from correlation functions
journal, March 2003


Many-Body Localization and Thermalization in Quantum Statistical Mechanics
journal, March 2015


Entanglement entropy scaling laws and eigenstate typicality in free fermion systems
journal, February 2015


Quantum statistical mechanics in a closed system
journal, February 1991


Chaos and quantum thermalization
journal, August 1994


Entanglement and off-diagonal long-range order of an η-pairing state
journal, May 2005


Phase diagram of the two-dimensional negative- U Hubbard model
journal, March 1989


Logarithmic divergence of the block entanglement entropy for the ferromagnetic Heisenberg model
journal, January 2005


Ground-state energy of the Hubbard model at half filling
journal, July 1996


Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
journal, December 2010


SO 4 SYMMETRY IN A HUBBARD MODEL
journal, June 1990