One-dimensional Bose gas in optical lattices of arbitrary strength

TL;DR

This paper investigates the phase diagram and physical properties of a one-dimensional Bose gas in optical lattices of arbitrary strength using exact numerical methods, comparing continuous and lattice models.

Contribution

It provides a comprehensive phase diagram for the continuous model and assesses the validity of the Bose-Hubbard and sine-Gordon models across lattice strengths.

Findings

Mapped the phase diagram of the continuous Bose gas model.

Identified the limitations of the sine-Gordon model for shallow lattices.

Determined the applicability regions of the Bose-Hubbard model.

Abstract

One-dimensional Bose gas with contact interaction in optical lattices at zero temperature is investigated by means of the exact diffusion Monte Carlo algorithm. The results obtained from the fundamental continuous model are compared with those obtained from the lattice (discrete) Bose-Hubbard model, using exact diagonalization, and from the quantum sine-Gordon model. We map out the complete phase diagram of the continuous model and determine the regions of applicability of the Bose-Hubbard model. Various physical quantities characterizing the systems are calculated and it is demonstrated that the sine-Gordon model used for shallow lattices is inaccurate.