Thermodynamics of one-dimensional SU(4) and SU(6) fermions with attractive interactions

TL;DR

This paper presents a nonperturbative study of thermodynamics in one-dimensional SU(4) and SU(6) fermionic systems with attractive interactions, predicting measurable effects of higher internal degrees of freedom on density and pressure.

Contribution

It provides the first finite-temperature lattice Monte Carlo calculations and a universal relation linking SU(2) and SU(N_f) systems, advancing understanding of nonperturbative correlations in these models.

Findings

Quantum effects influence thermodynamics despite dominant thermal fluctuations.

Additional degrees of freedom significantly increase density and pressure near zero chemical potential.

Results are directly applicable to current ultracold atom experiments in one-dimensional traps.

Abstract

Motivated by advances in the manipulation and detection of ultracold atoms with multiple internal degrees of freedom, we present a finite-temperature lattice Monte Carlo calculation of the density and pressure equations of state, as well as Tan's contact, of attractively interacting SU(4)- and SU(6)-symmetric fermion systems in one spatial dimension. We also furnish a nonperturbative proof of a universal relation whereby quantities computable in the SU(2) case completely determine the virial coefficients of the SU($N_f$) case. These one-dimensional systems are appealing because they can be experimentally realized in highly constrained traps and because of the dominant role played by correlations. The latter are typically nonperturbative and are crucial for understanding ground states and quantum phase transitions. While quantum fluctuations are typically overpowered by thermal ones in one and two dimensions at any finite temperature, we find that quantum effects do leave their imprint in thermodynamic quantities. Our calculations show that the additional degrees of freedom, relative to the SU(2) case, provide a dramatic enhancement of the density and pressure (in units of their noninteracting counterparts) in a wide region around vanishing $\beta\mu$, where $\beta$ is the inverse temperature and $\mu$ the chemical potential. As shown recently in experiments, the thermodynamics we explore here can be measured in a controlled and precise fashion in highly constrained traps and optical lattices. Our results are a prediction for such experiments in one dimension with atoms of high nuclear spin.