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

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.

11 pages, 7 figures; published version

References in corpus (17)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• A one-dimensional liquid of fermions with tunable spin
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• An exactly solvable model of the BCS-BEC crossover
• Phase Transitions and Pairing Signature in Strongly Attractive Fermi Atomic Gases
• Engineering the Dynamics of Effective Spin-Chain Models for Strongly Interacting Atomic Gases
• On the existence of the critical point in finite density lattice QCD
• Quantum-gas microscopes - A new tool for cold-atom quantum simulators
• Virial theorems for trapped cold atoms
• Universal contact for a Tonks-Girardeau gas at finite temperature
• High-momentum tails as magnetic structure probes for strongly-correlated $SU(\kappa )$ fermionic mixtures in one-dimensional traps
• Universality in one-dimensional fermions at finite temperature: Density, pressure, compressibility, and contact
• Critical phenomena in one dimension from a Bethe ansatz perspective
• Competing Valence Bond States of Spin-3/2 Fermions on a Strongly Coupled Ladder

Cited by in corpus (3)

• Universal Tan relations for quantum gases in one dimension
• Lattice Effective Field Theory Simulations of Nuclei
• Chiral Effective Field Theory after Thirty Years: Nuclear Lattice Simulations