Lieb-Liniger model with exponentially-decaying interactions: a continuous matrix product state study

TL;DR

This study extends the Lieb-Liniger model by replacing contact interactions with exponential decay, revealing new phases like quasi-crystals and super-Tonks-Girardeau states using continuous matrix product states.

Contribution

Introduces an extended Lieb-Liniger model with exponential interactions and explores its phase diagram using continuous matrix product states techniques.

Findings

Weak coupling exhibits superfluidity similar to original model

Strong coupling reveals quasi-crystal and super-Tonks-Girardeau regimes

The model shows a crossover between different quantum phases

Abstract

The Lieb-Liniger model describes one-dimensional bosons interacting through a repulsive contact potential. In this work, we introduce an extended version of this model by replacing the contact potential with a decaying exponential. Using the recently developed continuous matrix product states techniques, we explore the ground state phase diagram of this model by examining the superfluid and density correlation functions. At weak coupling superfluidity governs the ground state, in a similar way as in the Lieb-Liniger model. However, at strong coupling quasi-crystal and super-Tonks-Girardeau regimes are also found, which are not present in the original Lieb-Liniger case. Therefore the presence of the exponentially-decaying potential leads to a superfluid/super-Tonks-Girardeau/quasi-crystal crossover, when tuning the coupling strength from weak to strong interactions. This corresponds to a Luttinger liquid parameter in the range $K \in (0, \infty)$; in contrast with the Lieb-Liniger model, where $K \in [1, \infty)$, and the screened long-range potential, where $K \in (0, 1]$.