Spectrum of Dirac eigenvalues across QCD chiral transition

Ding, Heng-Tong; Huang, Wei-Ping; Mukherjee, Swagato; Petreczky, Peter

doi:10.1016/j.jspc.2025.100032

Spectrum of Dirac eigenvalues across QCD chiral transition

Journal Article · Tue Feb 11 00:00:00 EST 2025 · Journal of Subatomic Particles and Cosmology

DOI:https://doi.org/10.1016/j.jspc.2025.100032· OSTI ID:2587873

Ding, Heng-Tong ^[1]; Huang, Wei-Ping ^[1]; Mukherjee, Swagato ^[2]; ^[2]

Central China Normal University, Wuhan (China)
Brookhaven National Laboratory (BNL), Upton, NY (United States)

Here, we show that the universal scaling properties of the chiral phase transition in quantum chromodynamics (QCD) at the macroscale are encoded in the microscopic energy levels of the quarks in the background of gluon fields, defined as eigenvalues of the Dirac operator. We introduce a novel relation between the cumulants of 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 using HISQ action with varying light quark masses around the chiral phase transition temperature, 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.

View Accepted Manuscript (DOE)

Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0012704

OSTI ID:: 2587873

Alternate ID(s):: OSTI ID: 2560521

Report Number(s):: BNL--228561-2025-JAAM

Journal Information:: Journal of Subatomic Particles and Cosmology, Journal Name: Journal of Subatomic Particles and Cosmology Vol. 3; ISSN 3050-4805

Publisher:: Elsevier BVCopyright Statement

Country of Publication:: United States

Language:: English

References (16)

Chiral symmetry breaking in confining theories Banks, T.; Casher, A. Nuclear Physics B, Vol. 169, Issue 1-2 https://doi.org/10.1016/0550-3213(80)90255-2	journal	June 1980
A tool kit for staggered fermions Kilcup, G. W.; Sharpe, Stephen R. Nuclear Physics B, Vol. 283 https://doi.org/10.1016/0550-3213(87)90285-9	journal	January 1987
Finite-size-scaling functions for 3d O(4) and O(2) spin models and QCD Engels, J.; Holtmann, S.; Mendes, T. Physics Letters B, Vol. 514, Issue 3-4 https://doi.org/10.1016/S0370-2693(01)00798-5	journal	August 2001
QCD transition at the physical point, and its scaling window from twisted mass Wilson fermions Kotov, Andrey Yu.; Lombardo, Maria Paola; Trunin, Anton Physics Letters B, Vol. 823 https://doi.org/10.1016/j.physletb.2021.136749	journal	December 2021
The order of the quantum chromodynamics transition predicted by the standard model of particle physics Aoki, Y.; Endrődi, G.; Fodor, Z. Nature, Vol. 443, Issue 7112 https://doi.org/10.1038/nature05120	journal	October 2006
Chiral symmetry breaking and the Banks-Casher relation in lattice QCD with Wilson quarks Giusti, Leonardo; Lüscher, Martin Journal of High Energy Physics, Vol. 2009, Issue 03 https://doi.org/10.1088/1126-6708/2009/03/013	journal	March 2009
Sensitivity of the Polyakov loop and related observables to chiral symmetry restoration Clarke, D. A.; Kaczmarek, O.; Karsch, F. Physical Review D, Vol. 103, Issue 1 https://doi.org/10.1103/PhysRevD.103.L011501	journal	January 2021
Chiral phase transition in three-flavor QCD from lattice QCD Dini, Lorenzo; Hegde, Prasad; Karsch, Frithjof Physical Review D, Vol. 105, Issue 3 https://doi.org/10.1103/PhysRevD.105.034510	journal	February 2022
Curvature of the chiral phase transition line from the magnetic equation of state of ( 2+1 )-flavor QCD Ding, H. -T.; Kaczmarek, O.; Karsch, F. Physical Review D, Vol. 109, Issue 11 https://doi.org/10.1103/PhysRevD.109.114516	journal	June 2024
Remarks on the chiral phase transition in chromodynamics Pisarski, Robert D.; Wilczek, Frank Physical Review D, Vol. 29, Issue 2 https://doi.org/10.1103/PhysRevD.29.338	journal	January 1984
Magnetic equation of state in ( 2 + 1 )-flavor QCD Ejiri, S.; Karsch, F.; Laermann, E. Physical Review D, Vol. 80, Issue 9 https://doi.org/10.1103/PhysRevD.80.094505	journal	November 2009
QCD Phase Transition with Chiral Quarks and Physical Quark Masses Bhattacharya, Tanmoy; Buchoff, Michael I.; Christ, Norman H. Physical Review Letters, Vol. 113, Issue 8 https://doi.org/10.1103/PhysRevLett.113.082001	journal	August 2014
Chiral Phase Transition Temperature in ( 2 + 1 )-Flavor QCD Ding, H. -T.; Hegde, P.; Kaczmarek, O. Physical Review Letters, Vol. 123, Issue 6 https://doi.org/10.1103/PhysRevLett.123.062002	journal	August 2019
Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD Ding, H. -T.; Li, S. -T.; Mukherjee, Swagato Physical Review Letters, Vol. 126, Issue 8 https://doi.org/10.1103/PhysRevLett.126.082001	journal	February 2021
Microscopic Encoding of Macroscopic Universality: Scaling Properties of Dirac Eigenspectra near QCD Chiral Phase Transition Ding, H. -T.; Huang, W. -P.; Mukherjee, Swagato Physical Review Letters, Vol. 131, Issue 16 https://doi.org/10.1103/PhysRevLett.131.161903	journal	October 2023
Thermodynamics of strong-interaction matter from lattice QCD Ding, Heng-Tong; Karsch, Frithjof; Mukherjee, Swagato International Journal of Modern Physics E, Vol. 24, Issue 10 https://doi.org/10.1142/S0218301315300076	journal	October 2015