Lattice simulation with the Majorana positivity

Abstract

While the sign problem of the Dirac fermion is conditioned by the semipositivity of a determinant, that of the Majorana fermion is conditioned by the semipositivity of a Pfaffian. We introduce one sufficient condition for the semi-positivity of a Pfaffian. Based on the semi-positivity condition, we study an effective model of the Majorana fermion. We also present the application to the Dirac fermion.