• Open Access

Zero-temperature phases of the two-dimensional Hubbard-Holstein model: A non-Gaussian exact diagonalization study

Yao Wang, Ilya Esterlis, Tao Shi, J. Ignacio Cirac, and Eugene Demler
Phys. Rev. Research 2, 043258 – Published 19 November 2020

Abstract

We propose a numerical method which embeds the variational non-Gaussian wave-function approach within exact diagonalization, allowing for efficient treatment of correlated systems with both electron-electron and electron-phonon interactions. Using a generalized polaron transformation, we construct a variational wave function that absorbs entanglement between electrons and phonons into a variational non-Gaussian transformation; exact diagonalization is then used to treat the electronic part of the wave function exactly, thus taking into account high-order correlation effects beyond the Gaussian level. Keeping the full electronic Hilbert space, the complexity is increased only by a polynomial scaling factor relative to the exact diagonalization calculation for pure electrons. As an example, we use this method to study ground-state properties of the two-dimensional Hubbard-Holstein model, providing evidence for the existence of intervening phases between the spin and charge-ordered states. In particular, we find one of the intervening phases has strong charge susceptibility and binding energy, but is distinct from a charge-density-wave ordered state, while the other intervening phase displays superconductivity at weak couplings. This method, as a general framework, can be extended to treat excited states and dynamics, as well as a wide range of systems with both electron-electron and electron-boson interactions.

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  • Received 18 November 2019
  • Revised 28 October 2020
  • Accepted 30 October 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.043258

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yao Wang1,2,*, Ilya Esterlis1, Tao Shi3,4,†, J. Ignacio Cirac5,6, and Eugene Demler1

  • 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
  • 2Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29631, USA
  • 3CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 4CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100049, China
  • 5Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse. 1, 85748 Garching, Germany
  • 6Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 München, Germany

  • *yaowang@g.clemson.edu
  • tshi@mail.itp.ac.cn

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Vol. 2, Iss. 4 — November - December 2020

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