Equation of state of non-relativistic matter from automated perturbation theory and complex Langevin
arXiv:1710.05020 · doi:10.1051/epjconf/201817503007
Abstract
We calculate the pressure and density of polarized non-relativistic systems of two-component fermions coupled via a contact interaction at finite temperature. For the unpolarized one-dimensional system with an attractive interaction, we perform a third-order lattice perturbation theory calculation and assess its convergence by comparing with hybrid Monte Carlo. In that regime, we also demonstrate agreement with real Langevin. For the repulsive unpolarized one-dimensional system, where there is a so-called complex phase problem, we present lattice perturbation theory as well as complex Langevin calculations. For our studies, we employ a Hubbard-Stratonovich transformation to decouple the interaction and automate the application of Wick's theorem for perturbative calculations, which generates the diagrammatic expansion at any order. We find excellent agreement between the results from our perturbative calculations and stochastic studies in the weakly interacting regime. In addition, we show predictions for the strong coupling regime as well as for the polarized one-dimensional system. Finally, we show a first estimate for the equation of state in three dimensions where we focus on the polarized unitary Fermi gas.
8 pages, 6 figures, proceedings of Lattice2017, Granada, Spain
References in corpus (9)
- Many-Body Physics with Ultracold Gases
- Theory of ultracold Fermi gases
- Quantum Monte Carlo Simulations of the BCS-BEC Crossover at Finite Temperature
- A Unitary Fermi Supersolid: The Larkin-Ovchinnikov Phase
- Thermodynamics of a Trapped Unitary Fermi Gas
- Phase structure of mass- and spin-imbalanced unitary Fermi gases
- Phase structure of spin-imbalanced unitary Fermi gases
- Universality in one-dimensional fermions at finite temperature: Density, pressure, compressibility, and contact
- Imaginary polarization as a way to surmount the sign problem in ab initio calculations of spin-imbalanced Fermi gases