William J. Porter

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

We present finite-temperature, lattice Monte Carlo calculations of the particle number density, compressibility, pressure, and Tans 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.

Surmounting the sign problem in non-relativistic calculations: a case study with mass-imbalanced fermions

The calculation of the ground state and thermodynamics of mass-imbalanced Fermi systems is a challenging many-body problem. Even in one spatial dimension, analytic solutions are limited to special configurations and numerical progress with standard Monte Carlo approaches is hindered by the sign problem. The focus of the present work is on the further development of methods to study imbalanced systems in a fully non-perturbative fashion. We report our calculations of the ground-state energy of mass-imbalanced fermions using two different approaches which are also very popular in the context of the theory of the strong interaction (Quantum Chromodynamics, QCD): (a) the hybrid Monte Carlo algorithm with imaginary mass imbalance, followed by an analytic continuation to the real axis; and (b) the Complex Langevin algorithm. We cover a range of on-site interaction strengths that includes strongly attractive as well as strongly repulsive cases which we verify with non-perturbative renormalization group methods and perturbation theory. Our findings indicate that, for strong repulsive couplings, the energy starts to flatten out, implying interesting consequences for short-range and high-frequency correlation functions. Overall, our results clearly indicate that the Complex Langevin approach is very versatile and works very well for imbalanced Fermi gases with both attractive and repulsive interactions.

Entanglement, noise, and the cumulant expansion

We put forward a simpler and improved variation of a recently proposed method to overcome the signal-to-noise problem found in Monte Carlo calculations of the entanglement entropy of interacting fermions. The present method takes advantage of the approximate log-normal distributions that characterize the signal-to-noise properties of other approaches. In addition, we show that a simple rewriting of the formalism allows circumvention of the inversion of the restricted one-body density matrix in the calculation of the nth Rényi entanglement entropy for n>2. We test our technique by implementing it in combination with the hybrid Monte Carlo algorithm and calculating the n=2,3,4,⋯,10 Rényi entropies of the one-dimensional attractive Hubbard model. We use that data to extrapolate to the von Neumann (n=1) and n→∞ cases.

Tan's contact and the phase distribution of repulsive Fermi gases: Insights from quantum chromodynamics noise analyses

Path-integral analyses originally pioneered in the study of the complex-phase problem afflicting lattice calculations of finite-density quantum chromodynamics are generalized to non-relativistic Fermi gases with repulsive interactions. Using arguments similar to those previously applied to relativistic theories, we show that the analogous problem in nonrelativistic systems manifests itself naturally in Tans contact as a nontrivial cancellation between terms with varied dependence on extensive thermodynamic quantities. We analyze that case under the assumption of gaussian phase distribution, which is supported by our Monte Carlo calculations and perturbative considerations. We further generalize these results to observables other than the contact, as well as to polarized systems and systems with fixed particle number. Our results are quite general in that they apply to repulsive multi-component fermions, are independent of dimensionality or trapping potential, and hold in the ground state as well as at finite temperature.

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

We calculate the ground-state properties of unpolarized two-dimensional attractive fermions in the range from few to many particles. Using first-principles lattice Monte Carlo methods, we determine the ground-state energy, Tans contact, momentum distribution, and single-particle correlation function. We investigate those properties for systems of

Evolution from few- to many-body physics in one-dimensional Fermi systems: One- and two-body density matrices and particle-partition entanglement

N=4,8,\ensuremath{\cdots},40

Thermodynamics of one-dimensional SU(4) and SU(6) fermions with attractive interactions

particles and for a wide range of attractive couplings. As the attractive coupling is increased, the thermodynamic limit is reached at progressively lower

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

N

Convexity of the entanglement entropy of SU(2N)-symmetric fermions with attractive interactions.

due to the dominance of the two-body sector. At large momenta

Few-fermion systems in one dimension: Ground- and excited-state energies and contacts

k