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

• URL: http://arxiv.org/abs/2508.01692v1
• Date: Sun, 03 Aug 2025 09:51:35 GMT
• Title: Bose-Hubbard model in the canonical ensemble: a beyond mean-field approach
• Authors: Tista Banerjee,
• Abstract summary: In this paper, we consider an ansatz wave-function which respects total particle-number conservation for quantum many-body systems.<n>This wave-function has the same complexity in the number of parameters as the mean-field Gutzwiller ansatz.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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