Matter-Antimatter Coexistence Method for Finite Density QCD toward a Solution of the Sign Problem

Abstract

Toward the lattice QCD calculation at finite density, we propose “matter-antimatter coexistence method”, where matter and anti-matter systems are prepared on two parallel R 4 -sheets in five-dimensional Euclidean space-time. We put a matter system M with a chemical potential μ∈ C on a R 4 -sheet, and also put an anti-matter system with on the other R 4 -sheet shifted in the fifth direction. Between the gauge variables in M and in , we introduce a correlation term with a real parameter λ . In one limit of , a strong constraint is realized, and therefore the total fermionic determinant becomes real and non-negative, due to the cancellation of the phase factors in M and , although this system resembles QCD with an isospin chemical potential. In another limit of , this system goes to two separated ordinary QCD systems with the chemical potential of μ and . For a given finite-volume lattice, if one takes an enough large value of λ , is realized and phase cancellation approximately occurs between two fermionic determinants in M and , which suppresses the sign problem and is expected to make the lattice calculation possible. For the obtained gauge configurations of the coexistence system, matter-side quantities are evaluated through their measurement only for the matter part M . The physical quantities in finite density QCD are expected to be estimated by the calculations with gradually decreasing λ and the extrapolation to λ=0 . We also consider more sophisticated improvement of this method using an irrelevant-type correlation.