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

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.

19 pages, no figure, v2: references added, derivation elaborated, v3: accepted version for publication in PTEP

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Cited by in corpus (5)

• Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD
• Non-Hermitian Hubbard model without the sign problem
• Semigroup approach to the sign problem in quantum Monte Carlo simulations
• Quantum Monte Carlo simulation of a two-dimensional Majorana lattice model
• Lattice simulation with the Majorana positivity