2026/02/27 by Ravi Shanker, Anonymous, Harshit Pandey +1
Physics and Astronomy · #Quantum Chromodynamics and Particle Interactions #High-Energy Particle Collisions Research #Physics of Superconductivity and Magnetism
paper · pdf · doi:10.1103/571b-lm3m
We perform a comprehensive study of the properties of the Dirac eigenvalue spectrum in QCD as a function of temperature on the lattice. In addition to effects due to the interplay between interactions and disorder inherently present in a many-body system, the Dirac spectrum also contains crucial information about the effective restoration of different subgroups of almost exact two-flavor chiral symmetry in QCD. We calculate the infrared eigenvalues of the overlap Dirac operator on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>2</a:mn> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:mrow> </a:math> flavor QCD ensembles generated using domain wall fermion discretization, on a large volume lattice. From the normalized level spacing ratios, we identify those eigenvalues that have intermediate level statistics, distinctly different from the majority in the bulk spectrum that follow universal level fluctuations similar to a random matrix of Gaussian unitary type. We provide an explanation of these intermediate level ratios in terms of a specific random matrix model and quantify the correlation between these eigenstates and disorder in the gauge fields manifested in the renormalized Polyakov loop values. Whereas the existence of eigenmodes is intimately connected to the restoration of different subgroups of chiral symmetry close to the chiral crossover transition, their origin can be traced to random uncorrelated disorder at higher temperatures when the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>U</c:mi> <c:mi>A</c:mi> </c:msub> <c:mo stretchy="false">(</c:mo> <c:mn>1</c:mn> <c:mo stretchy="false">)</c:mo> </c:math> is . We also, for the first time, calculate the Thouless conductance for the Dirac spectrum that quantifies the structural rigidity of the eigenvectors, and use it as a diagnostic tool to understand the restoration of the anomalous <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>U</g:mi> <g:mi>A</g:mi> </g:msub> <g:mo stretchy="false">(</g:mo> <g:mn>1</g:mn> <g:mo stretchy="false">)</g:mo> </g:math> subgroup of chiral symmetry and localization driven by disorder.