Complex spectrum of finite-density lattice QCD with static quarks at strong coupling

Abstract

We calculate the spectrum of transfer matrix eigenvalues associated with Polyakov loops in finite-density lattice QCD with static quarks. These eigenvalues determine the spatial behavior of Polyakov loop correlations functions. Our results are valid for all values of the gauge coupling in $1+1$ dimensions, and valid in the strong-coupling region for any number of dimensions. When the quark chemical potential $\mu$ is nonzero, the spatial transfer matrix $T_s$ is non-Hermitian. The appearance of complex eigenvalues in $T_s$ is a manifestation of the sign problem in finite-density QCD. The invariance of finite-density QCD under the combined action of charge conjugation $\mathcal{C}$ and complex conjugation $\mathcal{K}$ implies that the eigenvalues of $T_s$ are either real or part of a complex pair. Calculation of the spectrum confirms the existence of complex pairs in much of the temperature-chemical potential plane. Many features of the spectrum for static quarks are determined by a particle-hole symmetry. For $\mu$ small compared to the quark mass $M$, we typically find real eigenvalues for the lowest lying states. At somewhat larger values of $\mu ,$ pairs of eigenvalues may form complex-conjugate pairs, leading to damped oscillatory behavior in Polyakov loop correlation functions. However, near $\mu =M$, the low-lying spectrum becomes real again. This is a direct consequence of the approximate particle-hole symmetry at $\mu =M$ for heavy quarks. This behavior of the eigenvalues should be observable in lattice simulations and can be used as a test of lattice algorithms. Our results provide independent confirmation of results we have previously obtained in PNJL models using complex saddle points.

14 pages, 11 figures. Figure 1 fixed, references added, minor editing and typos corrected

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Cited by in corpus (8)

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• $\mathcal{P}T$ symmetry, pattern formation, and finite-density QCD
• Dual formulations of Polyakov loop lattice models
• Persistent homology analysis for dense QCD effective model with heavy quarks
• Dual simulation of a Polyakov loop model at finite baryon density: phase diagram and local observables
• Liquid-Gas Phase Transitions and $\mathcal{C}\mathcal{K}$ Symmetry in Quantum Field Theories
• Dilepton production from moaton quasiparticles
• Duals of lattice Abelian models with static determinant at finite density