# Classification of sign-problem-free relativistic fermions on the basis of the Majorana positivity

## TL;DR

This paper classifies sign-problem-free relativistic fermion actions using Majorana representation, revealing new classes of such actions based on Pfaffian semi-positivity, which aids in quantum simulations.

## Contribution

It introduces a classification framework for sign-problem-free fermion actions using Majorana representation and derives new classes with Majorana-type sources.

## Key findings

- Sign-problem-free conditions are characterized by Pfaffian semi-positivity.
- Existing sign-problem-free actions can be understood via Pfaffian semi-positivity.
- New classes of sign-problem-free actions with Majorana sources are identified.

## Abstract

We classify the sign-problem-free relativistic fermion actions on the basis of the Majorana representation. In the Majorana representation, the sign-problem-free condition is given by the semi-positivity of a Pfaffian. We show that the known sign-problem-free actions of the Dirac fermions, which are usually understood from the semi-positivity of a determinant, e.g., the action of quantum chromodynamics with nonzero chiral chemical potential or nonzero isospin chemical potential, can also be understood from the semi-positivity of a Pfaffian. We also derive new classes of the sign-problem-free relativistic fermion actions with Majorana-type source terms.