Mitigating the sign problem for non-relativistic fermions on the lattice

Claudio Albanese, Nilanjana Datta

Mark Alford, Andrei B. Kryjevski

We study the fermion sign problem in a theory of non-relativistic fermions with a spin-independent repulsive interaction. We work in polar co-ordinates in momentum space, which makes it straightforward to keep only the low-energy degrees of freedom close to the Fermi surface. This is sufficient for the purpose of calculating many physically important low-energy observables. We find indications that the sign problem in this effective theory will be weaker than in the full theory, so low-energy properties of the theory could be calculated by modifying the action to make it positive semi-definite and including reweighting factors in the observables. We discuss suitable modifications of the action, and describe a possible lattice realization of the polar momentum space formulation of the theory.

Hersh Singh

We study the physics of two species of non-relativistic hard-core bosons with attractive or repulsive delta function interactions on a spacetime lattice using the worldline formulation. By tuning the chemical potential carefully we show that worm algorithms can efficiently sample the worldline configurations in any fixed particle-number sector. Since fermions can be treated as hard-core bosons up to a permutation sign, we also apply this approach to non-relativistic fermions. The fermion permutation sign is treated as an observable in this approach and can be used to extract energies for each particle-number sector. Since in one dimension non-relativistic fermions can only permute due to boundary effects, unlike the auxiliary field method, in many cases our approach does not suffer from sign problems. Using our method we discover limitations of the recently proposed complex Langevin calculations in one dimension.

Shailesh Chandrasekharan A

Tomoya Hayata, Yoshimasa Hidaka, Arata Yamamoto

Abstract We perform real-time lattice simulation of an open quantum system based on the Schwinger–Keldysh path integral representation of the Lindblad formalism. Although the real-time simulation generally suffers from the sign problem, a few exceptional cases exist. We focus on a sign-problem-free system of a non-relativistic spinless fermion and analyze the time evolution under driving and dissipation.

Józef Spałek, Adam Rycerz, W. Wójcik +1 more