Are the Tonks regimes in the continuum and on the lattice truly equivalent?

TL;DR

This paper compares the Tonks regimes in continuum and lattice systems, showing that lattice systems reach the Tonks regime more rapidly in terms of long-distance correlations, with detailed analysis of local correlations versus temperature and filling.

Contribution

It provides a detailed comparison of the Tonks regimes in lattice and continuum systems, highlighting differences in correlation behaviors and the conditions for entering the Tonks regime.

Findings

Local two-body correlations saturate with temperature in the lattice.

Long-distance correlations reach the Tonks regime faster on the lattice.

Lattice systems exhibit more rapid entry into the Tonks regime than continuum systems.

Abstract

Motivated by recent experiments, we compare the Tonks (i.e. hard-core boson gas) regime achieved in an optical lattice with the Tonks regime of a one-dimensional Bose gas in the continuum. For the lattice gas, we compute the local (i.e. on-site) two-body correlations as a function of temperature and the filling of the lattice. It is found that this function saturates to a constant value with increasing temperature. Furthermore, the parameter that characterizes the long-distance correlations in the lattice Tonks regime is also obtained, showing that on the lattice the long-distance correlations enter the Tonks regime more rapidly than in the continuum.