On the Lieb-Liniger model in the infinite coupling constant limit

TL;DR

This paper analyzes the Lieb-Liniger model in the infinite coupling limit, showing it behaves like free fermions and cannot distinguish bosonic features in experiments with atomic gases in one dimension.

Contribution

It demonstrates that in the infinite coupling limit, the Lieb-Liniger model is equivalent to free fermions, clarifying the model's physical implications and experimental limitations.

Findings

Model becomes indistinguishable from free fermions at infinite coupling

Bose-Einstein condensate experiments cannot detect bosonic characteristics in this limit

Wavefunctions vanish at particle coincidence points, mimicking fermionic behavior

Abstract

We consider the one-dimensional Lieb-Liniger model (bosons interacting via 2-body delta potentials) in the infinite coupling constant limit (the so-called Tonks-Girardeau model). This model might be relevant as a description of atomic Bose gases confined in a one-dimensional geometry. It is known to have a fermionic spectrum since the N-body wavefunctions have to vanish at coinciding points, and therefore be symmetrizations of fermionic Slater wavefunctions. We argue that in the infinite coupling constant limit the model is indistinguishable from free fermions, i.e., all physically accessible observables are the same as those of free fermions. Therefore, Bose-Einstein condensate experiments at finite energy that preserve the one-dimensional geometry cannot test any bosonic characteristic of such a model.