Microscopic Encoding of Macroscopic Universality: Scaling Properties of Dirac Eigenspectra near QCD Chiral Phase Transition

Abstract

Macroscopic properties of the strong interaction near its chiral phase transition exhibit scaling behaviors, which are the same as those observed close to the magnetic transition in a 3-dimensional classical spin system with $O(4)$ symmetry. We show that the universal scaling properties of the chiral phase transition in Quantum Chromodynamics (QCD) at the macroscale are, in fact, encoded within the microscopic energy levels of its fundamental constituents, the quarks. We establish a connection between the cumulants of the chiral order parameter, i.e., the chiral condensate, and the correlations among the energy levels of quarks, i.e., the eigenspectra of the massless QCD Dirac operator. This relation elucidates how the fluctuations of the chiral condensate arise from the correlations within the infrared part of the energy spectra of quarks, and naturally leads to a generalization of the Banks-Casher relation for the cumulants of the chiral condensate. Then, through (2+1)-flavor lattice QCD calculations with varying light quark masses near the QCD chiral transition, we demonstrate that the correlations among the infrared part of the Dirac eigenvalue spectra exhibit same universal scaling behaviors as expected of the cumulants of the chiral condensate. We find that these universal scaling behaviors extend up to the physical values of the up and down quark masses. Our study reveals how the hidden scaling features at the microscale give rise to the macroscopic universal properties of QCD.

5 pages main text + 3 pages supplemental material, version to appear in PRL

References in corpus (7)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The equation of state in (2+1)-flavor QCD
• The QCD Equation of State to $\mathcal{O}({\mu }_B^6)$ from Lattice QCD
• The Sphaleron Rate in the Minimal Standard Model
• Scaling studies of QCD with the dynamical HISQ action
• Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks
• U(2)xU(2)-symmetric fixed point from the Functional Renormalization Group

Cited by in corpus (4)

• Soft modes in hot QCD matter
• Curvature of the chiral phase transition line from the magnetic equation of state of (2+1)-flavor QCD
• Unified Functional-Holographic Theory of the QCD Critical End Point
• Microscopic Encoding of Macroscopic Universality in QCD Chiral Phase Transition