Virial coefficients of trapped and un-trapped three-component fermions with three-body forces in arbitrary spatial dimensions

Abstract

Using a coarse temporal lattice approximation, we calculate the first few terms of the virial expansion of a three-species fermion system with a three-body contact interaction in $d$ spatial dimensions, both in homogeneous space as well as in a harmonic trapping potential of frequency $\omega$. Using the three-body problem to renormalize, we report analytic results for the change in the fourth- and fifth-order virial coefficients $\Delta b_4$ and $\Delta b_5$ as functions of $\Delta b_3$. Additionally, we argue that in the $\omega \to 0$ limit the relationship $b_n^{\text{T}}=n^{-d/2}{b}_n$ holds between the trapped (T) and homogeneous coefficients for arbitrary temperature and coupling strength (not merely in scale-invariant regimes). Finally, we point out an exact, universal (coupling- and frequency-independent) relationship between $\Delta b_3^{\text{T}}$ in 1D with three-body forces and $\Delta b_2^{\text{T}}$ in 2D with two-body forces.

arXiv comment7 pages, 2 figures

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• The fourth- and fifth-order virial coefficients from weak-coupling to unitarity
• Thermodynamics and static response of anomalous 1D fermions via quantum Monte Carlo in the worldline representation
• Fourth- and fifth-order virial expansion of harmonically trapped fermions at unitarity
• Efimov-like physics in fraction-dimensional Bose systems with three-body interaction
• Quantum anomaly and thermodynamics of one-dimensional fermions with antisymmetric two-body interactions
• Toward an automated-algebra framework for high orders in the virial expansion of quantum matter