Bosons in optical lattices - from the Mott transition to the Tonks-Girardeau gas

TL;DR

This paper uses quantum Monte Carlo simulations to study the crossover of trapped bosons in optical lattices from a softcore gas to a Tonks-Girardeau regime, revealing that Tonks-Girardeau behavior appears at relatively low interaction strengths.

Contribution

It demonstrates that the Tonks-Girardeau regime can be reached without a finite critical interaction strength and compares the efficiency of two quantum Monte Carlo methods for large systems.

Findings

Tonks-Girardeau behavior observed at low interaction strengths

No finite critical interaction value for the crossover

Comparison of Monte Carlo methods for efficiency

Abstract

We present results from quantum Monte Carlo simulations of trapped bosons in optical lattices, focusing on the crossover from a gas of softcore bosons to a Tonks-Girardeau gas in a one-dimensional optical lattice. We find that depending on the quantity being measured, the behavior found in the Tonks-Girardeau regime is observed already at relatively small values of the interaction strength. A finite critical value for entering the Tonks-Girardeau regime does not exist. Furthermore, we discuss the computational efficiency of two quantum Monte Carlo methods to simulate large scale trapped bosonic systems: directed loops in stochastic series expansions and the worm algorithm.