arXiv subjects

C. R. Shill

Publications and source records attributed to C. R. Shill.

4 recordsLinked to original sources

arXiv2020

Leading- and next-to-leading order semiclassical approximation to the first seven virial coefficients of spin-1/2 fermions across spatial dimensions

Following up on recent calculations, we investigate the leading- and next-to-leading order semiclassical approximation to the virial coefficients of a two-species fermion system with a contact interaction. Using the analytic result for the second-order virial coefficient as a renormalization condition, we derive expressions for up to the seventh-order virial coefficient $Δb_7$. Our results at leading order, though approximate, furnish simple analytic formulas that relate $Δb_n$ to $Δb_2$ for arbitrary dimension, providing a glimpse into the behavior of the virial expansion across dimensions and coupling strengths. As an application, we calculate the pressure and Tan's contact of the 2D attractive Fermi gas and examine the radius of convergence of the virial expansion as a function of the coupling strength.

cond-mat.quant-gas↗

arXiv2018

Virial coefficients of 1D and 2D Fermi gases by stochastic methods and a semiclassical lattice approximation

We map out the interaction effects on the first six virial coefficients of one-dimensional Fermi gases with zero-range attractive and repulsive interactions, and the first four virial coefficients of the two-dimensional analog with attractive interactions. To that end, we use two non-perturbative stochastic methods: projection by complex stochastic quantization, which allows us to determine high-order coefficients at weak coupling and estimate the radius of convergence of the virial expansion; and a path-integral representation of the virial coefficients. To complement our numerical calculations, we present leading-order results in a semiclassical lattice approximation, which we find to be surprisingly close to the expected answers.

cond-mat.quant-gas↗

arXiv2017

Particle Projection Using a Complex Langevin Method

Using complex stochastic quantization, we implement a particle-number projection technique on the partition function of spin-1/2 fermions at finite temperature on the lattice. We discuss the method, its application towards obtaining the thermal properties of finite Fermi systems in three spatial dimensions, and results for the first five virial coefficients of one-dimensional, attractively interacting fermions.

hep-lat↗

arXiv2016

Ground-state energy, density profiles, and momentum distribution of attractively interacting 1D Fermi gases with hard-wall boundaries: a Monte Carlo study

Motivated by the realization of hard-wall boundary conditions in experiments with ultracold atoms, we investigate the ground-state properties of spin-1/2 fermions with attractive interactions in a one-dimensional box. We use lattice Monte Carlo methods to determine essential quantities like the energy, which we compute as a function of coupling strength and particle number in the regime from few to many particles. Many-fermion systems bound by hard walls display non-trivial density profiles characterized by so-called Friedel oscillations (which are similar to those observed in harmonic traps). In non-interacting systems, the characteristic length scale of the oscillations is set by (2 kF)^(-1), where kF is the Fermi momentum, while repulsive interactions tend to generate Wigner-crystal oscillations of period (4 kF)^(-1). Based on the non-interacting result, we find a remarkably simple parametrization of the density profiles of the attractively interacting case, which we generalize to the one-body density matrix. While the total momentum is not a conserved quantity in the presence of hard walls, the magnitude of the momentum does provide a good quantum number. We are therefore able to provide a detailed characterization of the (quasi-)momentum distribution, which displays rather robust discontinuity at the Fermi surface. In addition, we determine the spatially varying on-site density-density correlation, which in turn yields Tan's contact density and, upon integration, Tan's contact. As is well known, the latter fully determines the short-range correlations and plays a crucial role in a multitude of equilibrium and non-equilibrium sum rules.

cond-mat.quant-gas↗