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Related papers: Spectral Fluctuations of the QCD Dirac Operator

200 papers

We discuss properties of thermal Quantum Chromodynamics obtained by means of lattice simulations with overlap fermions. This fermion discretisation preserves chiral symmetry at finite lattice spacing. We present details of the formulation…

High Energy Physics - Lattice · Physics 2025-10-30 Z. Fodor , A. Yu. Kotov , T. G. Kovacs , K. K. Szabo

We study the distribution of the phase angle and the magnitude of the fermion determinant as well as its correlation with the chiral condensate and the baryon number for QCD at non-zero quark chemical potential. Results are derived to…

High Energy Physics - Lattice · Physics 2010-03-19 M. P. Lombardo , K. Splittorff , J. J. M. Verbaarschot

We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac operator using both chiral Perturbation Theory and chiral Random Matrix Theory. A graded chiral Lagrangian is used to evaluate the microscopic…

High Energy Physics - Lattice · Physics 2015-03-17 G. Akemann , P. H. Damgaard , K. Splittorff , J. J. M. Verbaarschot

We reveal 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…

High Energy Physics - Lattice · Physics 2024-01-22 Heng-Tong Ding , Wei-Ping Huang , Swagato Mukherjee , Peter Petreczky

In this lecture we discuss some exact results for the low-lying spectrum of the Dirac operator in adjoint QCD. In particular, we find an analytical expression for the slope of the average spectral density. These results are obtained by…

High Energy Physics - Theory · Physics 2007-05-23 D. Toublan , J. J. M. Verbaarschot

We consider the parity-invariant Dirac operator with a mass term in three-dimensional QCD for $N_c=2$ and quarks in the fundamental representation. We show that there exists a basis in which the matrix elements of the Euclidean Dirac…

High Energy Physics - Theory · Physics 2009-10-31 Ulrika Magnea

The chiral condensate in QCD at zero temperature does not depend on the quark chemical potential (up to one third the nucleon mass), whereas the spectral density of the Dirac operator shows a strong dependence on the chemical potential. The…

High Energy Physics - Theory · Physics 2009-02-23 J. C. Osborn , K. Splittorff , J. J. M. Verbaarschot

We compare the low-lying spectrum of the staggered Dirac operator in the confining phase of compact U(1) gauge theory on the lattice to predictions of chiral random matrix theory. The small eigenvalues contribute to the chiral condensate…

High Energy Physics - Lattice · Physics 2009-10-31 B. A. Berg , H. Markum , R. Pullirsch , T. Wettig

The relation between the spectral density of the QCD Dirac operator at nonzero baryon chemical potential and the chiral condensate is investigated. We use the analytical result for the eigenvalue density in the microscopic regime which…

High Energy Physics - Theory · Physics 2009-11-11 J. C. Osborn , K. Splittorff , J. J. M. Verbaarschot

We link the spontaneous breakdown of chiral symmetry in Euclidean QCD to the collision of spectral shock waves in the vicinity of zero eigenvalue of Dirac operator. The mechanism, originating from complex Burger's-like equation for viscid,…

High Energy Physics - Phenomenology · Physics 2015-12-23 Jean-Paul Blaizot , Maciej A. Nowak , Piotr Warchoł

A brief overview of the lattice technique of studying QCD is presented. Recent results from the UKQCD Collaboration's simulations with dynamical quarks are then presented. In this work, the calculations are all at a fixed lattice spacing…

High Energy Physics - Phenomenology · Physics 2009-11-07 Chris Allton

We show that the lowest part of the eigenvalue density of the staggered fermion operator in lattice QCD_3 at small lattice coupling constant beta has exactly the same shape as in QCD_4. This observation is quite surprising, since universal…

High Energy Physics - Lattice · Physics 2011-02-28 P. Bialas , Z. Burda , B. Petersson

We investigate the universality of microscopic eigenvalue correlations for Random Matrix Theories with the global symmetries of the QCD partition function. In this article we analyze the case of real valued chiral Random Matrix Theories…

High Energy Physics - Theory · Physics 2008-11-26 B. Klein , J. J. M. Verbaarschot

We analyze the eigenvalue spectrum of the staggered Dirac matrix in two-color QCD at nonzero baryon density when the eigenvalues become complex. The quasi-zero modes and their role for chiral symmetry breaking and the deconfinement…

High Energy Physics - Lattice · Physics 2009-10-31 Elmar Bittner , Maria-Paola Lombardo , Harald Markum , Rainer Pullirsch

In quantum field theories, spectral densities are directly related to relevant physical observables. In Lattice QCD, their non-perturbative extraction from first principles requires the Inverse Laplace transform of Euclidean-time…

High Energy Physics - Lattice · Physics 2025-01-29 Matteo Saccardi , Mattia Bruno , Leonardo Giusti

Temporal quark correlation functions are analyzed in quenched lattice QCD for two values of temperature above the critical temperature (Tc) for deconfinement, T=1.5Tc and 3Tc. A two-pole ansatz for the quark spectral function is used to…

High Energy Physics - Lattice · Physics 2013-05-30 Olaf Kaczmarek , Frithjof Karsch , Masakiyo Kitazawa , Wolfgang Soeldner

Recently, Kalkreuter obtained complete Dirac spectra for $SU(2)$ lattice gauge theory both for staggered fermions and for Wilson fermions. The lattice size was as large as $12^4$. We performed a statistical analysis of these data and found…

High Energy Physics - Lattice · Physics 2008-11-26 M. A. Halasz , T. Kalkreuter , J. J. M. Verbaarschot

We study discretization effects of the Wilson and staggered Dirac operator with $N_{\rm c}>2$ using chiral random matrix theory (chRMT). We obtain analytical results for the joint probability density of Wilson-chRMT in terms of a…

High Energy Physics - Lattice · Physics 2012-02-09 Mario Kieburg , Jacobus J. M. Verbaarschot , Savvas Zafeiropoulos

In lattice QCD spectrum calculations, it is desirable to obtain multiple excited state energies in each symmetry channel. Typically, one constructs several interpolating operators for the symmetry channel of interest, forms the `correlator…

High Energy Physics - Lattice · Physics 2008-11-26 Adam C. Lichtl

We reconsider constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature. To avoid possible ultra-violet(UV) divergences, we work on a lattice, employing the overlap Dirac…

High Energy Physics - Lattice · Physics 2013-05-30 Sinya Aoki , Hidenori Fukaya , Yusuke Taniguchi