Properties of the one-dimensional Bose-Hubbard model from a high-order perturbative expansion

TL;DR

This paper uses high-order perturbative expansion to analyze the ground state properties of the one-dimensional Bose-Hubbard model in the Mott phase, providing analytical insights and comparing with numerical results.

Contribution

It introduces a high-order perturbative approach to characterize the Bose-Hubbard model's ground state and discusses a new sum rule for density correlations.

Findings

Perturbative expansion accurately describes ground state properties in certain regimes.

Comparison with numerical simulations validates the analytical approach.

A new sum rule for density-density correlations is proposed.

Abstract

We employ a high-order perturbative expansion to characterize the ground state of the Mott phase of the one-dimensional Bose-Hubbard model. We compute for different integer filling factors the energy per lattice site, the two-point and density-density correlations, and expectation values of powers of the on-site number operator determining the local atom number fluctuations (variance, skewness, kurtosis). We compare these expansions to numerical simulations of the infinite-size system to determine their range of applicability. We also discuss a new sum rule for the density-density correlations that can be used in both equilibrium and non-equilibrium systems.