Equation of state of non-relativistic matter from automated perturbation theory and complex Langevin
- Mr. Andrew LOHEAC
- Mr. Andrew LOHEAC (University of North Carolina at Chapel Hill)
We calculate the pressure and density equations of state of both unpolarized and polarized non-relativistic fermions at finite temperature in 1D. For attractive contact interactions, where there is no sign problem, we perform a third-order lattice perturbation theory calculation, assess its convergence properties by comparing with hybrid Monte Carlo, and demonstrate agreement with real Langevin. For repulsive contact interactions, we present lattice perturbation theory as well as complex Langevin calculations, with a modified action to prevent uncontrolled excursions in the complex plane. In our perturbative approach, we use a Hubbard-Stratonovich transformation to decouple the interaction and automate the application of Wick's theorem, thus generating the diagrammatic expansion at any desired order. We find exceptional agreement between perturbative and non-perturbative results at weak couplings, and furnish predictions based on complex Langevin at strong couplings. Both the lattice perturbation theory and complex Langevin formalisms can easily be extended to a variety of situations including bosons and higher dimensions.
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Applications Beyond QCD