Impenetrable SU(N) fermions in one-dimensional lattices

TL;DR

This paper investigates SU(N) fermions with infinite on-site repulsion in 1D lattices, revealing that their one-body correlations decay Gaussianly at zero temperature and stretched exponentially at finite temperatures, differing from typical 1D systems.

Contribution

It introduces an exact numerical method for calculating correlations in a novel model of distinguishable quantum particles derived from SU(N) fermions.

Findings

Ground state one-body correlations decay Gaussianly with distance.

Finite-temperature correlations follow a stretched exponential decay.

The model exhibits unique correlation decay behavior compared to typical 1D systems.

Abstract

We study SU(N) fermions in the limit of infinite on-site repulsion between all species. We focus on states in which every pair of consecutive fermions carries a different spin flavor. Since the particle order cannot be changed (because of the infinite on-site repulsion) and contiguous fermions have a different spin flavor, we refer to the corresponding constrained model as the model of distinguishable quantum particles. We introduce an exact numerical method to calculate equilibrium one-body correlations of distinguishable quantum particles based on a mapping onto noninteracting spinless fermions. In contrast to most many-body systems in one dimension, which usually exhibit either power-law or exponential decay of off-diagonal one-body correlations with distance, distinguishable quantum particles exhibit a Gaussian decay of one-body correlations in the ground state, while finite-temperature correlations are well described by stretched exponential decay.