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Related papers: Spectral Density of the QCD Dirac Operator near Ze…

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We calculate the spectral density of the Dirac operator over an ensemble of configurations composed of overlapping instantons and anti-instantons. We find evidence that the spectral density diverges in the limit of small eigenvalues. This…

High Energy Physics - Lattice · Physics 2009-10-31 U. Sharan , M. Teper

We discuss the eigenvalue distribution of the overlap Dirac operator in quenched QCD on lattices of size 8^{4}, 10^{4} and 12^{4} at \beta = 5.85 and \beta = 6. We distinguish the topological sectors and study the distributions of the…

High Energy Physics - Lattice · Physics 2009-11-10 W. Bietenholz , K. Jansen , S. Shcheredin

Chiral random matrix theory makes very detailed predictions for the spectral correlations of the QCD Dirac operator, both in the bulk of the spectrum and near zero virtuality. These predictions have been successfully tested in lattice QCD…

High Energy Physics - Lattice · Physics 2007-05-23 Tilo Wettig

In a deep-infrared (ergodic) regime, QCD coupled to massive pseudoreal and real quarks are described by chiral orthogonal and symplectic ensembles of random matrices. Using this correspondence, general expressions for the QCD partition…

High Energy Physics - Theory · Physics 2009-10-31 T. Nagao , S. M. Nishigaki

We investigate the spectral properties of the Wilson Dirac operator in quenched QCD in the microscopic regime. We distinguish the topological sectors using the index as determined by the Wilson flow method. Consequently, the distributions…

High Energy Physics - Lattice · Physics 2012-01-04 Albert Deuzeman , Urs Wenger , Jair Wuilloud

Aoki, Fukaya, and Taniguchi claim that both the spectral density of the Dirac operator at the origin and the topological susceptibility must vanish identically for sufficiently small but nonzero mass $m$ in the chirally symmetric phase of…

High Energy Physics - Lattice · Physics 2025-10-29 Matteo Giordano

The inverse eigenvalues of the Dirac operator in the Schwinger model satisfy the same Leutwyler-Smilga sum rules as in the case of QCD with one flavor. In this paper we give a microscopic derivation of these sum rules in the sector of…

High Energy Physics - Theory · Physics 2009-11-11 L. Shifrin , J. J. M. Verbaarschot

We show how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero modes. It is no longer gamma_5-hermitian, but its nonreal eigenvalues still…

High Energy Physics - Lattice · Physics 2009-01-14 Jacques Bloch , Tilo Wettig

We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) and U(1) gauge theory as well as in full QCD with two colors and finite chemical potential. Along the strong-coupling axis up to the phase transition, the…

High Energy Physics - Lattice · Physics 2008-11-26 Elmar Bittner , Maria-Paola Lombardo , Harald Markum , Rainer Pullirsch

Random matrix theory and chiral Lagrangians offer a convenient tool for the exact calculation of microscopic spectral correlators of the Dirac operator in a well-defined finite-volume scaling regime.

High Energy Physics - Lattice · Physics 2009-10-31 P. H. Damgaard

Exact results from random matrix theory are used to systematically analyse the relationship between microscopic Dirac spectra and finite-volume partition functions. Results are presented for the unitary ensemble, and the chiral analogs of…

High Energy Physics - Theory · Physics 2009-10-31 G. Akemann , P. H. Damgaard

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

In the epsilon-regime of QCD the main features of the spectrum of the low-lying eigenvalues of the (euclidean) Dirac operator are expected to be described by a certain universality class of random matrix models. In particular, the latter…

High Energy Physics - Lattice · Physics 2009-11-10 Leonardo Giusti , Martin Lüscher , Peter Weisz , Hartmut Wittig

Quark spectra in QCD are linked to fundamental properties of the theory including the identification of pions as the Goldstone bosons of spontaneously broken chiral symmetry. The lattice Overlap-Dirac operator provides a nonperturbative,…

High Energy Physics - Theory · Physics 2009-10-31 Robert G. Edwards , Urs M. Heller , Joe Kiskis , Rajamani Narayanan

We show that at the critical point of chiral random matrix models, novel scaling laws for the inverse moments of the eigenvalues are expected. We evaluate explicitly the pertinent microscopic spectral density, and found it in agreement with…

High Energy Physics - Phenomenology · Physics 2015-06-25 R. A. Janik , M. A. Nowak , G. Papp , I. Zahed

We investigate the replica trick for the microscopic spectral density, $\rho_s(x)$, of the Euclidean QCD Dirac operator. Our starting point is the low-energy limit of the QCD partition function for $n$ fermionic flavors (or replicas) in the…

High Energy Physics - Theory · Physics 2008-11-26 D. Dalmazi , J. J. M Verbaarschot

We use a random matrix model to study chiral symmetry breaking in QCD at finite chemical potential $\mu$. We solve the model and compute the eigenvalue density of the Dirac matrix on a complex plane. A naive ``replica trick'' fails for…

High Energy Physics - Lattice · Physics 2009-10-28 M. A. Stephanov

In this talk we present the results published recently in Ref. [1], where we showed how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero…

High Energy Physics - Lattice · Physics 2009-01-14 Jacques Bloch , Tilo Wettig

We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD as well as in quenched U(1) theory on various lattice sizes. As a measure of the fluctuation properties of the eigenvalues, we study…

High Energy Physics - Lattice · Physics 2007-05-23 Bernd A. Berg , Harald Markum , Rainer Pullirsch , Tilo Wettig

We develop a theoretical approach to compute the conditioned spectral density of $N \times N$ non-invariant random matrices in the limit $N \rightarrow \infty$. This large deviation observable, defined as the eigenvalue distribution…

Disordered Systems and Neural Networks · Physics 2018-08-15 Isaac Pérez Castillo , Fernando L. Metz