Exact solution of a 1D many-body system with momentum dependent interactions

TL;DR

This paper presents an exact solution for a 1D many-body system with momentum-dependent interactions, linking it to the non-relativistic limit of the massive Thirring model and exploring its solvability.

Contribution

It establishes an exact solution for a specific 1D many-body model and investigates its relation to known integrable models and dualities.

Findings

Fermionic case maps to the non-relativistic massive Thirring model

The fermionic model can be solved exactly via a mapping to the 1D boson gas

Generalization to distinguishable particles is not exactly solvable by Bethe ansatz

Abstract

We discuss a 1D many-body model of distinguishable particles with local, momentum dependent two-body interactions. We show that the restriction of this model to fermions corresponds to the non-relativistic limit of the massive Thirring model. This fermion model can be solved exactly by a mapping to the 1D boson gas with inverse coupling constant. We provide evidence that this mapping is the non-relativistic limit of the duality between the massive Thirring model and the quantum sine-Gordon model. We also investigate the question if the generalization of this model to distinguishable particles is exactly solvable by the coordinate Bethe ansatz and find that this is not the case.