Related papers: Dirac eigenvalue correlations in quenched QCD at f…
We report on our ongoing effort to understand quenched lattice QCD at finite baryon number density. The quenched theory is sensitive to the baryon mass both at strong coupling and in the scaling region. However, we find that the quenched…
I extend to QCD an efficient method for lattice gauge theory with dynamical fermions. Once the eigenvalues of the Dirac operator and the density of states of pure gluonic configurations at a set of plaquette energies (proportional to the…
The quark number density at finite imaginary chemical potential is investigated in the lattice QCD using the Dirac-mode expansion. We find the analytical formula of the quark number density in terms of the Polyakov loop in the large quark…
We derive exact analytical expressions for the spectral density of the Dirac operator at fixed \theta-angle in the microscopic domain of one-flavor QCD. These results are obtained by performing the sum over topological sectors using novel…
The distribution of individual Dirac eigenvalues is derived by relating them to the density and higher eigenvalue correlation functions. The relations are general and hold for any gauge theory coupled to fermions under certain conditions…
We study the properties of low-lying Dirac modes in quenched compact QED at $\beta$=0.99, 1.01 and 1.03, employing $12^3\times 12$ lattices and the overlap formalism for the fermion action. We pay special attention to the spatial…
I describe a mechanism to understand the relation between chiral-symmetry breaking and eigenmodes of the Dirac operator in lattice QCD with Kogut-Susskind sea quarks. It can be shown that if chiral symmetry is spontaneously broken, the…
The Banks--Casher relation links the spontaneous breaking of chiral symmetry in QCD to the presence of a non-zero density of quark modes at the low end of the spectrum of the Dirac operator. Spectral observables like the number of modes in…
We report on the results of our calculation of meson correlators in a finite volume. The calculation is carried out in the quenched approximation near the chiral limit (down to Mq = 2.6 MeV) using the overlap fermion. For these small quark…
The overlap Dirac operator, which satisfies the Ginsparg-Wilson relation, realizes exact chiral symmetry on the lattice without any unphysical doubler modes. To perform the path integrals, one should, however, note that the overlap fermion…
Using the graded eigenvalue method and a recently computed extension of the Itzykson-Zuber integral to complex matrices, we compute the $k$-point spectral correlation functions of the Dirac operator in a chiral random matrix model with a…
The order parameter of the chiral phase transition is directly related to the infrared part of the spectrum of the QCD Dirac operator. This part of the spectrum follows from the low energy limit of QCD which is given by a partition function…
Aiming at the link between confinement and chiral symmetry the Polyakov loop represented as a spectral sum of eigenvalues of the Dirac operator was subject of recent studies. We analyze the volume dependence as well as the continuum…
We evaluate equal time point to point spatial correlation functions of mesonic currents at finite temperature. For this purpose we consider the QCD vacuum structure in terms of quark antiquark condensates and their fluctuations in terms of…
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…
We study effective energies of heavy-light meson correlation functions in lattice QCD and a small volume of (0.2 fm)^4 to non-perturbatively calculate their dependence on the heavy quark mass in the continuum limit. Our quenched results…
We investigate the distribution of the spacings of adjacent eigenvalues of the lattice Dirac operator. At zero chemical potential $\mu$, the nearest-neighbor spacing distribution $P(s)$ follows the Wigner surmise of random matrix theory…
For theories with a sign problem there is no analog of the Banks-Casher relation. This is true in particular for QCD at nonzero quark chemical potential. However, for QCD-like theories without a sign problem the Banks-Casher relation can be…
We compute the low lying spectrum of the overlap Dirac operator in the deconfined phase of finite-temperature quenched gauge theory. It suggests the existence of a chiral condensate which we confirm with a direct stochastic estimate. We…
We calculate numerically the eigenvalue distribution of the overlap Dirac operator in the quenched Schwinger model on a lattice. The distribution does not fit any of the three universality classes of spontaneous chiral symmetry breaking,…