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

Journal Article · Tue Dec 26 00:00:00 EST 2017 · SciPost Physics

DOI:https://doi.org/10.21468/SciPostPhys.3.6.043· OSTI ID:1414843

Vafek, Oskar ^[1]; Regnault, Nicolas ^[2]; Bernevig, B. Andrei ^[3]

---

1. Florida State University, National High Magnetic Field Laboratory, Princeton University
2. Sorbonne University, École Normale Supérieure, Princeton University
3. Princeton University

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.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0016239
• OSTI ID: 1414843
• Journal Information: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 6 Vol. 3; ISSN 2542-4653
• Publisher: Stichting SciPost
• Country of Publication: Netherlands
• Language: English