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

Abstract

We newly propose "matter-antimatter coexistence (MAC) method" for the lattice QCD calculation at finite density, as a possible solution of the sign problem. For the matter system $M$ with $\mu > 0$, we also prepare the anti-matter system $\bar M$ with $-\mu < 0$ in the other spatial location. The number of degrees of freedom in $M$ is set to be just the same as that in $\bar M$. Here, we need not impose charge conjugation symmetry for the fields between $M$ and $\bar M$. In this coexistence system, the total generating functional $Z_{M+\bar M}$ becomes real and non-negative in Euclidean space-time. Then, we only have to deal with its real part ${\rm Re}Z_{M+\bar M} (\ge 0)$, i.e., the real part of the total fermionic determinant, ${\rm Re Det} K$. This advanced point is expected to reduce the sign problem significantly and to enable the numerical calculation in lattice QCD. Through the lattice QCD measurement only for the matter part $M$, one can obtain physical quantities in finite density QCD with $\mu > 0$.