Spin-incoherent Luttinger liquid of one-dimensional SU($\kappa$) fermions

TL;DR

This paper explores the properties of one-dimensional SU(κ) fermions in the spin-incoherent regime, using numerical simulations to analyze their momentum distributions and compare with analytical predictions, relevant for experiments with alkaline-earth fermions.

Contribution

It provides a theoretical framework for understanding spin-incoherent SU(κ) fermions in the Tonks-Girardeau limit, including numerical methods and comparison with analytical results.

Findings

Momentum distributions are broadened by strong interactions.

Increasing κ reduces broadening for fixed N, but increases it for fixed particles per spin.

High momentum tails follow a 1/p^4 decay, matching analytical predictions.

Abstract

We theoretically investigate one-dimensional (1D) SU($\kappa$) fermions in the regime of spin-incoherent Luttinger liquid. We specifically focus on the Tonks-Girardeau gas limit where its density is sufficiently low that effective repulsions between atoms become infinite. In such case, spin exchange energy of 1D SU($\kappa$) fermions vanishes and all spin configurations are degenerate, which automatically puts them into spin-incoherent regime. In this limit, we are able to express the single-particle density matrices in terms of those of anyons. This allows us to numerically simulate the number of particles up to $N=32$. We numerically calculate single-particle density matrices in two cases: (1) equal populations for each spin components (balanced) and (2) all $S_z$ manifolds included. In contrast to noninteracting multi-component fermions, the momentum distributions are broadened due to strong interactions. As $\kappa$ increases, the momentum distributions are less broadened for fixed $N$, while they are more broadened for fixed number of particle per spin component. We then compare numerically calculated high momentum tails with analytical predictions which are proportional to $1/p^4$, in good agreement. Thus, our theoretical study provides a comparison with the experiments of repulsive multicomponent alkaline-earth fermions with a tunable SU($\kappa$) spin-symmetry in the spin-incoherent regime.