Related papers: Distribution law of the Dirac eigenmodes in QCD
I discuss recent results on the relation between the localisation of low-lying Dirac eigenmodes, the restoration of chiral symmetry, and deconfinement in QCD and QCD-like models, providing evidence of a close connection between the three…
In many of the experimental systems that may host Majorana zero modes, a so-called chiral symmetry exists that protects overlapping zero modes from splitting up. This symmetry is operative in a superconducting nanowire that is narrower than…
We present some of the reasoning and results substantiating the notion that spontaneous chiral symmetry breaking (SChSB) in QCD is encoded in local chiral properties of Dirac eigenmodes. Such association is possible when viewing chirality…
We study the effect of topology for a random matrix model of QCD at nonzero imaginary chemical potential or nonzero temperature. Non-universal fluctuations of Dirac eigenvalues lead to normalization factors that contribute to the…
We report tests and results from a new approach to the spectral density and the mode number distribution of the Dirac operator in lattice gauge theories. The algorithm generates the spectral density of the lattice Dirac operator as a…
In this lecture we give a brief review of chiral Random Matrix Theory (chRMT) and its applications to QCD at nonzero chemical potential. We present both analytical arguments involving chiral perturbation theory and numerical evidence from…
We analyze the statistical properties of the spectrum of the QCD Dirac operator at low energy in a finite box of volume $L^4$ by means of partially quenched Chiral Perturbation Theory (pqChPT), a low-energy effective field theory based on…
The low-lying eigenvalue spectrum of the QCD Dirac operator in the epsilon-regime is expected to match with that of chiral Random Matrix Theory (ChRMT). We study this correspondence for the case including sea quarks by performing two-flavor…
To understand the relation between the chiral symmetry breaking and monopoles, the chiral condensate which is the order parameter of the chiral symmetry breaking is calculated in the $\overline{\mbox{MS}}$ scheme at 2 [GeV]. First, we add…
We study some interesting aspects of the spectral properties of SU(3) gauge theory, both with and without dynamical quarks (QCD) at thermal equilibrium using lattice gauge theory techniques. By calculating the eigenstates of a massless…
The correlations of the QCD Dirac eigenvalues are studied with use of an extended chiral random matrix model. The inclusion of spatial dependence which the original model lacks enables us to investigate the effects of diffusion modes. We…
We apply the complex Langevin (CL) method to a chiral random matrix theory (ChRMT) at non-zero chemical potential and study the nearest neighbor spacing (NNS) distribution of the Dirac eigenvalues. The NNS distribution is extracted using an…
We establish a relationship between the zeros of the partition function in the complex mass plane and the spectral properties of the Dirac operator in QCD. This relation is derived within the context of chiral Random Matrix Theory and…
One of the most challenging issues in QCD is the investigation of spontaneous chiral-symmetry breaking, which is characterized by the non-vanishing chiral condensate when the bare fermion mass is zero. In standard methods, one has to…
We report on experimental studies that were performed with a microwave Dirac billiard (DB), that is, a flat resonator containing metallic cylinders arranged on a triangular grid, whose shape has a threefold rotational C3 symmetry. Its band…
We discuss the construction and properties of an approximate solution of the Ginsparg-Wilson equation, the so-called chirally improved lattice Dirac operator. In particular we study the behavior of its eigenmodes in smooth instanton…
We propose a simple instanton-based random matrix model of hot QCD that in the quenched case precisely reproduces the distribution of the lowest lattice overlap Dirac eigenvalues. Even after including dynamical quarks the model can be…
The Dirac fermion in the random chiral models is studied which includes the random gauge field model and the random hopping model. We focus on a connection between continuum and lattice models to give a clear perspective for the random…
The spontaneous breaking of chiral symmetry in QCD is known to be linked to a non-zero density of eigenvalues of the massless Dirac operator near the origin. Numerical studies of two-flavour QCD now suggest that the low quark modes are…
In this paper we study a random matrix model with the chiral and flavor structure of the QCD Dirac operator and a temperature dependence given by the lowest Matsubara frequency. Using the supersymmetric method for random matrix theory, we…