Universality in one-dimensional fermions at finite temperature: Density, pressure, compressibility, and contact

Abstract

We present finite-temperature, lattice Monte Carlo calculations of the particle number density, compressibility, pressure, and Tan's contact of an unpolarized system of short-range, attractively interacting spin-1/2 fermions in one spatial dimension, i.e., the Gaudin-Yang model. In addition, we compute the second-order virial coefficients for the pressure and the contact, both of which are in excellent agreement with the lattice results in the low-fugacity regime. Our calculations yield universal predictions for ultracold atomic systems with broad resonances in highly constrained traps. We cover a wide range of couplings and temperatures and find results that support the existence of a strong-coupling regime in which the thermodynamics of the system is markedly different from the noninteracting case. We compare and contrast our results with identical systems in higher dimensions.

Thermal equation of state of polarized fermions in one dimension via complex chemical potentials

“…The associated systematic effects should, in principle, be further investigated, although the results of our previous work [24] indicate that those effects are below 10%. We consider our present work as a proofof-principle study of our imaginary spin-imbalance approach.…”

“…[21][22][23], but reduced to one spatial dimension and generalized to complex chemical potentials as explained above (see also Ref. [24]). Because one-dimensional problems are computationally inexpensive, it is possible to calculate in very large lattices, e.g.…”

“…For such a coupling strength, a lattice size of N x = 61, which we fixed throughout this study, is sufficient to provide a good quantitative understanding of the continuum limit (see Ref. [24]). The physical extent of the system is L = N x , where = 1 fixes the spatial lattice units.…”

“…where Q 1,0 = L/λ T and Q 1,1 and Q 2,0 may be determined by direct calculation [24]. Note that the expansion coefficients Q N ↑ ,N ↓ depend implicitly on the coupling λ.…”

Ground state of the two-dimensional attractive Fermi gas: Essential properties from few to many body

“…[48]; closely related methods were used to examine systems in 1D in Ref. [49] and in 3D in Ref. [50].…”