Something interacting and solvable in 1d

TL;DR

This paper introduces a new family of exactly solvable 1D quantum many-body models, extending the Lieb-Liniger model, with detailed analysis of their scattering, ground states, and excitation spectra.

Contribution

It constructs a two-parameter family of solvable models in 1D quantum systems, generalizing known models and exploring their spectral and scattering properties.

Findings

Derived Bethe equations for ground states.

Identified spectrum inversion phenomena for certain parameters.

Connected models via $SL(2)$ transformations and generalized point interactions.

Abstract

We present a two-parameter family of exactly solvable quantum many-body systems in one spatial dimension containing the Lieb-Liniger model of interacting bosons as a particular case. The principal building block of this construction is the previously-introduced (arXiv:1712.09375) family of two-particle scattering matrices. We discuss an $SL(2)$ transformation connecting the models within this family and make a correspondence with generalized point interactions. The Bethe equations for the ground state are discussed with a special emphasis on "non-interacting modes" connected by the modular subgroup of $SL(2)$. The bound state solutions are discussed and are conjectured to follow some correlated version of the string hypothesis. The excitation spectrum of the new models in this family is derived in analogy to the Lieb-Liniger model and we show that for certain choices of parameters a spectrum inversion occurs such that the Umklapp solutions become the new ground state.