Few interacting fermions in one-dimensional harmonic trap

TL;DR

This paper investigates the behavior of spin-1/2 fermions in a one-dimensional harmonic trap with contact interactions, analyzing degeneracy effects, thermalization signatures, and mechanisms to break degeneracy using exact diagonalization.

Contribution

It provides a detailed analysis of degeneracy and thermalization in interacting fermions in 1D traps, highlighting the effects of strong repulsive interactions.

Findings

Degeneracy occurs at strong repulsive interactions.

Level occupation numbers indicate thermalization.

Thermal effects and depolarizing channels influence system behavior.

Abstract

We study spin-1/2 fermions, interacting via a two-body contact potential, in a one-dimensional harmonic trap. Applying exact diagonalization, we investigate their behavior at finite interaction strength, and discuss the role of the ground-state degeneracy which occurs for sufficiently strong repulsive interaction. Even low temperature or a completely depolarizing channel may then dramatically influence the system's behavior. We calculate level occupation numbers as signatures of thermalization, and we discuss the mechanisms to break the degeneracy.