Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles

TL;DR

This paper classifies and solves exactly two families of 1D quantum many-body systems with local interactions, extending delta interactions to distinguishable particles and identifying new solutions to the Yang-Baxter relations.

Contribution

It identifies two new exactly solvable models of distinguishable particles in 1D with generalized local interactions, including explicit eigenfunctions and Yang-Baxter solutions.

Findings

Two families of exactly solvable models are found.

Explicit eigenfunctions are derived for one model.

A novel solution to Yang-Baxter relations is presented.

Abstract

As is well-known, there exists a four parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum dependent terms, and we determine all cases leading to many-body systems of distinguishable particles which are exactly solvable by the coordinate Bethe Ansatz. We find two such families of systems, one with two independent coupling constants deforming the well-known delta interaction model to non-identical particles, and the other with a particular one-parameter combination of the delta- and (so-called) delta-prime interaction. We also find that the model of non-identical particles gives rise to a somewhat unusual solution of the Yang-Baxter relations. For the other model we write down explicit formulas for all eigenfunctions.