Lattice theory for nonrelativistic fermions in one spatial dimension

Abstract

I derive a loop representation for the canonical and grand-canonical partition functions for an interacting four-component Fermi gas in one spatial dimension and an arbitrary external potential. The representation is free of the "sign problem" irrespective of population imbalance, mass imbalance, and to a degree, sign of the interaction strength. This property is in sharp contrast with the analogous three-dimensional two-component interacting Fermi gas, which exhibits a sign problem in the case of unequal masses, chemical potentials, and repulsive interactions. The one-dimensional system is believed to exhibit many phenomena in common with its three-dimensional counterpart, including an analog of the BCS-BEC crossover, and nonperturbative universal few- and many-body physics at scattering lengths much larger than the range of interaction, making the theory an interesting candidate for numerical study. Positivity of the probability measure for the partition function allows for a mean-field treatment of the model; here, I present such an analysis for the interacting Fermi gas in the SU(4) (unpolarized, mass-symmetric) limit, and demonstrate that there exists a phase in which a continuum limit may be defined.

12 pages, 6 figures, references added

References in corpus (22)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Universality in Few-body Systems with Large Scattering Length
• Large momentum part of fermions with large scattering length
• Energetics of a strongly correlated Fermi gas
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Worm algorithms for classical statistical models
• Nucleon-Nucleon Scattering from Effective Field Theory
• Nonrelativistic conformal field theories
• Itinerant Ferromagnetism in a Fermi Gas of Ultracold Atoms
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• The Loop Algorithm
• Auxiliary Field quantum Monte Carlo for Strongly Paired Fermions
• Universal Fermi gases in mixed dimensions
• Resonantly Interacting Fermions In a Box
• Exact Relations for a Strongly-interacting Fermi Gas near a Feshbach Resonance
• Polarization Measurements and the Pairing Gap in the Universal Regime
• BEC-BCS crossover and universal relations in unitary Fermi gases
• Momentum Distribution and Contact of the Unitary Fermi gas
• A lattice theory for low energy fermions at finite chemical potential
• Method for simulating O(N) lattice models at finite density
• Universal four-component Fermi gas in one dimension

Cited by in corpus (10)

• Approaches to the sign problem in lattice field theory
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Gauge and matter fields as surfaces and loops - an exploratory lattice study of the Z(3) Gauge-Higgs model
• Spin Polarized Non-Relativistic Fermions in 1+1 Dimensions
• New developments for dual methods in lattice field theory at non-zero density
• Thermodynamics and static response of anomalous 1D fermions via quantum Monte Carlo in the worldline representation
• Few-body physics on a space-time lattice in the worldline approach
• Transdimensional equivalence of universal constants for Fermi gases at unitarity
• Numerical study of unitary fermions in one spatial dimension
• The Hubbard model in the canonical formulation