Polarized fermions in one dimension: density and polarization from complex Langevin calculations, perturbation theory, and the virial expansion

Abstract

We calculate the finite-temperature density and polarization equations of state of one-dimensional fermions with a zero-range interaction, considering both attractive and repulsive regimes. In the path-integral formulation of the grand-canonical ensemble, a finite chemical potential asymmetry makes these systems intractable for standard Monte Carlo approaches due to the sign problem. Although the latter can be removed in one spatial dimension, we consider the one-dimensional situation in the present work to provide an efficient test for studies of the higher-dimensional counterparts. To overcome the sign problem, we use the complex Langevin approach, which we compare here with other approaches: imaginary-polarization studies, third-order perturbation theory, and the third-order virial expansion. We find very good qualitative and quantitative agreement across all methods in the regimes studied, which supports their validity.

arXiv comment9 pages, 6 figures

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• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Finite-temperature equation of state of polarized fermions at unitarity
• Complex Langevin simulations and the QCD phase diagram: Recent developments
• Emergence of a pseudogap in the BCS-BEC crossover
• Thermodynamics of spin-orbit coupled bosons in two dimensions from complex Langevin
• Pairing patterns in one-dimensional spin- and mass-imbalanced Fermi gases
• Virial coefficients of 1D and 2D Fermi gases by stochastic methods and a semiclassical lattice approximation
• The virial expansion of attractively interacting Fermi gases in 1D, 2D, and 3D, up to fifth order
• Complex Langevin study for polarons in an attractively interacting one-dimensional two-component Fermi gas
• Low-Dimensional Fluctuations and Pseudogap in Gaudin-Yang Fermi Gases
• A lattice pairing-field approach to ultracold Fermi gases
• Thermal liquid-gas phase transition in a quasi-one-dimensional dipolar Fermi gas