Lattice simulation with the Majorana positivity

TL;DR

This paper introduces a sufficient condition for the semi-positivity of a Pfaffian, enabling lattice simulations of Majorana fermions and exploring their effective models and applications to Dirac fermions.

Contribution

The paper proposes a new semi-positivity condition for Pfaffians, facilitating sign-problem-free lattice simulations of Majorana fermions.

Findings

Established a sufficient semi-positivity condition for Pfaffians.

Applied the condition to an effective Majorana fermion model.

Demonstrated potential applications to Dirac fermion simulations.

Abstract

While the sign problem of the Dirac fermion is conditioned by the semi-positivity of a determinant, that of the Majorana fermion is conditioned by the semi-positivity 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