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 βµ, where β is the inverse temperature and µ 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.

Chiral Effective Field Theory after Thirty Years: Nuclear Lattice Simulations

“…This approximate SU(4) symmetry for the attractive S-wave interactions suppresses the sign and phase oscillations of the matrix determinants. This has been studied in several papers, some of which also consider inequalities that can be proven as a consequence [51,52,17,53,38].…”

Universal Tan relations for quantum gases in one dimension

“…In 1D the 1/k 4 decay of the momentum distribution and the contact were investigated numerically and analytically for the Lieb-Liniger model [25][26][27][28][29][30][31][32][33][34][35][36][37][38], attractive and repulsive spin- 1 2 fermions [39][40][41][42][43][44][45][46][47][48][49][50], the fermionic polaron problem [43,[51][52][53], spin-1 2 bosons [39,54,55], spin-1 bosons [56,57], κ-component (κ > 2) fermions and mixtures [58][59][60][61][62], and impenetrable anyons [63][64][65]. Despite this intense activity a comprehensive set of Tan relations or an analytical derivation of the tail of the momentum distribution can be found in the literature only for the case of single-component bosons [5,33,…”

Tan's contact and the phase distribution of repulsive Fermi gases: Insights from quantum chromodynamics noise analyses

“…[36][37][38][39], placing the system on a Euclidean spacetime of extent N x × N τ periodic in the space and anti-periodic in (imaginary) time. As shown in Fig.…”

“…It was also shown that the contact appears in sum rules involving the shear and bulk viscosities, the superfluid density, and other response functions [28][29][30] (See also Refs. [31][32][33][34]). …”