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.
A novel lattice approach is presented for studying systems comprising a large number of interacting nonrelativistic fermions. The construction is ideally suited for numerical study of fermions near unitarity-a strongly coupled regime corresponding to the two-particle s-wave scattering phase shift δ0 = ≠/2. Such systems may be achieved experimentally with trapped atoms, and provide a starting point for an effective field theory description of nuclear physics. We discuss the construction of our lattice theory, which allows us to study systems of up to (but by no means limited to) 38 fermions with high accuracy and modest computational resources, and offer an overview of several applications of the technique. A more detailed discussion of applications and simulation results will be described in companion proceedings by A. N. N. and J-W. L.
A novel lattice approach is presented for studying systems comprising a large number of interacting nonrelativistic fermions.The construction is ideally suited for numerical study of fermions near unitarity-a strongly coupled regime corresponding to the two-particle s-wave scattering phase shift δ 0 = π/2.Such systems may be achieved experimentally with trapped atoms, and provide a starting point for an effective field theory description of nuclear physics.We discuss the construction of our lattice theory, which allows us to study systems of up to (but by no means limited to) 38 fermions with high accuracy and modest computational resources, and offer an overview of several applications of the technique.A more detailed discussion of applications and simulation results will be described in companion proceedings by A. N. N. and J-W.L.
Lattice field theory is a useful tool for studying strongly interacting theories in condensed matter physics.A prominent example is the unitary Fermi gas: a two-component system of fermions interacting with divergent scattering length.With Monte Carlo methods this system can be studied from first principles.In the presence of an imbalance (unequal number of particles in the two components) a sign problem arises, which makes conventional algorithms inapplicable.We will show how to apply reweighting techniques to generalise the recently developed worm algorithm to the imbalanced case, and present results for the critical temperature, the energy per particle, the chemical potential and the contact density for equal, as well as unequal number of fermions in the two spin components.
We present a nonperturbative computation of the equation of state of polarized, attractively interacting, nonrelativistic fermions in one spatial dimension at finite temperature. We show results for the density, spin magnetization, magnetic susceptibility, and Tan's contact. We compare with the second-order virial expansion, a next-to-leading-order lattice perturbation theory calculation, and interpret our results in terms of pairing correlations. Our lattice Monte Carlo calculations implement an imaginary chemical potential difference to avoid the sign problem. The thermodynamic results on the imaginary side are analytically continued to obtain results on the real axis. We focus on an intermediate- to strong-coupling regime, and cover a wide range of temperatures and spin imbalances.
Dilute Fermi systems with large
s-wave scattering length
as exhibit universal properties if the interparticle spacing
r0 greatly exceeds the range of the underlying two-body interaction potential. In this regime,
r0 is the only relevant length scale and observables such as the energy per particle depend only on
r0 (or, equivalently, the energy
EFG of the free Fermi gas). This paper investigates Bose and Fermi systems with nonvanishing angular momentum
l using the lowest order constrained variational method. We focus on the regime where the generalized scattering length becomes large and determine the relevant length scales. For Bose gases with large generalized scattering lengths, we obtain simple expressions for the energy per particle in terms of an
l-dependent length scale ${\ensuremath{\xi}}_{l}$, which depends on the range of the underlying two-body potential and the average interparticle spacing. We discuss possible implications for dilute two-component Fermi systems with finite
l. Furthermore, we determine the equation of state of liquid and gaseous bosonic helium.