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We revisit two-color two-flavor Quantum Chromodynamics (QCD) which suffers from the sign problem of the Dirac determinant at finite baryon or quark density if a finite isospin chemical potential breaks two-flavor degeneracy. We discuss the eigenvalue distribution of the single-flavor Dirac operator to find the quartet structure, i.e. if λ + m is an eigenvalue where m is the current quark mass in a continuum theory, λ ∗+ m, −λ + m, and−λ ∗+ m must be eigenvalues as well. As a result the product of these four eigenvalues makes a non-negative real number, unless λ is real. The sign problem remains harmful for real λ because not a quartet but a pair of λ +m and −λ +mappears then and its product is not necessarily non-negative. In such a case, however, the sign problem has a different nature from the ordinary one in three-color QCD at finite density. We can rather identify it as the sign problem in the parity broken (or Aoki) phase inherent in the Wilson fermion formalism.

Sign problem in two-color two-flavor QCD with quark and isospin chemical potentials