Multicomponent Strongly Interacting Few-Fermion Systems in One Dimension

TL;DR

This paper analyzes a one-dimensional multicomponent fermion system with strong interactions, providing analytical insights into its energy spectrum and wave functions, especially in the limit of infinite repulsion.

Contribution

It introduces an analytical approach to strongly interacting multicomponent fermions in one dimension, focusing on the degeneracy and wave functions of a three-particle system.

Findings

Infinite repulsion leads to sixfold degeneracy in energy spectrum.

Partial lifting of degeneracy occurs at finite large repulsion.

Wave functions are explicitly described for the three-particle system.

Abstract

The paper examines a trapped one-dimensional system of multicomponent spinless fermions that interact with a zero-range two-body potential. We show that when the repulsion between particles is very large the system can be approached analytically. To illustrate this analytical approach we consider a simple system of three distinguishable particles, which can be addressed experimentally. For this system we show that for infinite repulsion the energy spectrum is sixfold degenerate. We also show that this degeneracy is partially lifted for finitely large repulsion for which we find and describe corresponding wave functions.