Abstract
We calculate the pressure and density of polarized non-relativistic systems of two-component fermions coupled via a contact interaction at finite temperature. For the unpolarized one-dimensional system with an attractive interaction, we perform a thirdorder lattice perturbation theory calculation and assess its convergence by comparing with hybrid Monte Carlo. In that regime, we also demonstrate agreement with real Langevin. For the repulsive unpolarized one-dimensional system, where there is a so-called complex phase problem, we present lattice perturbation theory as well as complex Langevin calculations. For our studies, we employ a Hubbard-Stratonovich transformation to decouple the interaction and automate the application of Wick’s theorem for perturbative calculations, which generates the diagrammatic expansion at any order. We find excellent agreement between the results from our perturbative calculations and stochastic studies in the weakly interacting regime. In addition, we show predictions for the strong coupling regime as well as for the polarized one-dimensional system. Finally, we show a first estimate for the equation of state in three dimensions where we focus on the polarized unitary Fermi gas.
Highlights
It is well-known that a large number of physically interesting quantum many-body systems are not amenable to being studied with stochastic techniques due to the appearance of the sign problem
We address advances on both perturbative and non-perturbative methods to compute the equation of state (EOS) for a many-body system of spin-1/2 particles under two-body contact interactions in situations normally hampered by a sign problem
Proceeding to the repulsive case, where hybrid Monte Carlo (HMC) is not applicable, we see that complex Langevin (CL) results show once again excellent agreement with perturbation theory at weak coupling, and as the order in perturbation theory is increased, the agreement with CL improves substantially
Summary
It is well-known that a large number of physically interesting quantum many-body systems are not amenable to being studied with stochastic techniques due to the appearance of the sign problem. [1] for a review) In this proceeding, we address advances on both perturbative and non-perturbative methods to compute the equation of state (EOS) for a many-body system of spin-1/2 particles under two-body contact interactions in situations normally hampered by a sign (or even complex-phase) problem. We address advances on both perturbative and non-perturbative methods to compute the equation of state (EOS) for a many-body system of spin-1/2 particles under two-body contact interactions in situations normally hampered by a sign (or even complex-phase) problem These systems can be physically realized as ultracold atoms, which provide a clean and malleable experimental situation to benchmark methods as well as many-body theories (see, e.g., [2, 3]). We provide a first estimate for the finite-temperature particle density of the polarized Fermi gas at unitarity in Sec. 5, which corresponds to Eq (1) extended to three spatial dimensions and tuned to the threshold of bound-state formation
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