Bose-Hubbard model in the canonical ensemble: a beyond mean-field approach

TL;DR

This paper introduces a particle-number conserving ansatz wave-function for the Bose-Hubbard model that captures quantum correlations beyond mean-field theory, enabling the study of quantum phases and out-of-equilibrium dynamics.

Contribution

It proposes a novel, computationally efficient ansatz that respects particle number conservation and extends mean-field approaches to include quantum correlations and entanglement.

Findings

Accurately describes quantum phases in Bose-Hubbard systems.

Effectively models out-of-equilibrium dynamics after quenches.

Shows good agreement with exact diagonalization results.

Abstract

Ultracold atoms in optical lattices are versatile testbeds to study and manipulate equilibrium and out-of-equilibrium aspects of quantum many-body systems whose behavior can be described by Hubbard-type Hamiltonians. In this paper, we consider an ansatz wave-function which respects total particle-number conservation for such systems and goes beyond mean-field theory; this wave-function has the same complexity in the number of parameters as the mean-field Gutzwiller ansatz, and captures quantum correlations and entanglement via projection onto an effective low-energy manifold. This ansatz can be exploited to study quantum phases observed in a large class of systems realizable in such experimental platforms and is useful to study quantum dynamics. We show that the relaxation dynamics of various out-of-equilibrium initial states under sudden quench of Hamiltonian parameters can be studied with this ansatz wavefunction within the framework of time-dependent variational principle. We present a quantitative comparison with small-scale exact diagonalization results in the 1D Bose-Hubbard model with and without external trapping potentials.