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Berry-phase-induced canonical structure of quantum fluctuations across the Mott-superfluid phase diagram

Idan S. Wallerstein* and Eytan Grosfeld†

  • *Contact author: wallesrh@post.bgu.ac.il
  • †Contact author: grosfeld@bgu.ac.il
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Phys. Rev. Research 8, 033116 – Published 27 July, 2026

DOI: https://doi.org/10.1103/g274-2kj3

Abstract

We develop a unified field-theoretical description of the Bose-Hubbard model that captures low-energy dynamics across the insulator-to-superfluid transition. We show that commonly used cumulant expansions about the Mott ground state fail in the superfluid phase not only quantitatively but also fundamentally, because they impose an incorrect canonical structure. Expanding instead about the appropriate mean-field saddle point, we derive an effective action in which the dynamics of fluctuations are governed by a Berry-phase term, giving rise to an emergent magnetic field in the associated oscillator description. This field encodes particle-hole symmetry breaking in both the Mott-insulator phase and the superfluid, and vanishes at the point where a pure Goldstone mode emerges. The resulting effective hydrodynamic theory admits a speed of sound that approaches the Bogoliubov limit in the weakly interacting regime, demonstrating consistency across the entire phase diagram, from the Mott-insulator to the deep superfluid regime. While the total density remains continuous within mean-field theory, we find that quantum fluctuations generate a discontinuous contribution at the quantum phase transition, which vanishes at the tip of the Mott lobe.

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Phys. Rev. Research 8, 033116– Published 27 July, 2026
  • Received 7 May 2025
  • Accepted 28 May 2026
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