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

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...

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Bibliographic Details
Published in:Physical review. D 2018-09, Vol.98 (5), Article 054507
Main Authors: Loheac, Andrew C., Braun, Jens, Drut, Joaquín E.
Format: Article
Language:English
Subjects:
Chemical potential
Density
Equations of state
Fermions
Mathematical analysis
Organic chemistry
Perturbation methods
Perturbation theory
Polarization
Qualitative analysis
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Summary: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 that end, 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.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.98.054507