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Quantum fluctuations beyond the Gutzwiller approximation in the Bose-Hubbard model

Fabio Caleffi1,2,*, Massimo Capone1,3, Chiara Menotti2, Iacopo Carusotto2,4, and Alessio Recati2,4,†

  • 1International School for Advanced Studies (SISSA), I-34136 Trieste, Italy
  • 2INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy
  • 3CNR-IOM Democritos, I-34136 Trieste, Italy
  • 4Trento Institute for Fundamental Physics and Applications, INFN, 38123, Trento, Italy

  • *fcaleffi@sissa.it
  • †alessio.recati@cnr.it
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Phys. Rev. Research 2, 033276 – Published 20 August, 2020

DOI: https://doi.org/10.1103/PhysRevResearch.2.033276

Abstract

We develop a quantum many-body theory of the Bose-Hubbard model based on the canonical quantization of the action derived from a Gutzwiller mean-field ansatz. Our theory is a systematic generalization of the Bogoliubov theory of weakly interacting gases. The control parameter of the theory, defined as the zero point fluctuations on top of the Gutzwiller mean-field state, remains small in all regimes. The approach provides accurate results throughout the whole phase diagram, from the weakly to the strongly interacting superfluid and into the Mott insulating phase. As specific examples of application, we study the two-point correlation functions, the superfluid stiffness, and the density fluctuations, for which quantitative agreement with available quantum Monte Carlo data is found. In particular, the two different universality classes of the superfluid-insulator quantum phase transition at integer and noninteger filling are recovered.

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Phys. Rev. Research 2, 033276– Published 20 August, 2020
  • Received 9 August 2019
  • Accepted 29 July 2020
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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.

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