Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures

TL;DR

This paper calculates the dynamic structure factor and polarizability of a one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures, revealing the absence of superfluidity in this regime.

Contribution

It introduces an exact Bose-Fermi mapping and derives approximations for correlation functions, extending understanding of finite-temperature behavior near the Tonks-Girardeau limit.

Findings

Superfluidity is precluded at finite temperature in the large-b3 regime.

Dynamic and static structure factors are approximated at finite temperature.

Results are applicable to spinless fermions with weak p-wave interactions.

Abstract

Correlation functions related to the dynamic density response of the one-dimensional Bose gas in the model of Lieb and Liniger are calculated. An exact Bose-Fermi mapping is used to work in a fermionic representation with a pseudopotential Hamiltonian. The Hartree-Fock and generalized random phase approximations are derived and the dynamic polarizability is calculated. The results are valid to first order in 1/\gamma where \gamma is Lieb-Liniger coupling parameter. Approximations for the dynamic and static structure factor at finite temperature are presented. The results preclude superfluidity at any finite temperature in the large-\gamma regime due to the Landau criterion. Due to the exact Bose-Fermi duality, the results apply for spinless fermions with weak p-wave interactions as well as for strongly interacting bosons.