QED2 as a testbed for interpolations between quenched and full QCD

Lattice QED2 with the Wilson formulation of fermions is used as a convenient model system to study artifacts of the quenched approximation on a finite lattice. The quenched functional integral is shown to be ill-defined in this system as a consequence of the appearance of exactly real modes for physical values of the fermion mass. The location and frequency of such modes is studied as a function of lattice spacing, lattice volume, topological charge and improved action parameters. The efficacy of the recently proposed modified quenched approximation is examined, as well as a new approach to the interpolation from the quenched to full dynamical theory employing a truncated form of the fermion determinant.Comment: Talk presented by A. Duncan at LATTICE97 (theoretical developments

Interaction dependence of composite fermion effective masses

We estimate the composite fermion effective mass for a general two particle potential r^{-\alpha} using exact diagonalization for polarized electrons in the lowest Landau level on a sphere. Our data for the ground state energy at filling fraction \nu=1/2 as well as estimates of the excitation gap at \nu=1/3, 2/5 and 3/7 show that m_eff \sim \alpha^{-1}.Comment: 4 pages, RevTeX, 5 figure

Chirality Correlation within Dirac Eigenvectors from Domain Wall Fermions

In the dilute instanton gas model of the QCD vacuum, one expects a strong spatial correlation between chirality and the maxima of the Dirac eigenvectors with small eigenvalues. Following Horvath, {\it et al.} we examine this question using lattice gauge theory within the quenched approximation. We extend the work of those authors by using weaker coupling, $\beta=6.0$, larger lattices, $16^4$, and an improved fermion formulation, domain wall fermions. In contrast with this earlier work, we find a striking correlation between the magnitude of the chirality density, $|\psi^\dagger(x)\gamma^5\psi(x)|$, and the normal density, $\psi^\dagger(x)\psi(x)$, for the low-lying Dirac eigenvectors.Comment: latex, 25 pages including 12 eps figure

Are Topological Charge Fluctuations in QCD Instanton Dominated?

We consider a recent proposal by Horv\'ath {\em et al.} to address the question whether topological charge fluctuations in QCD are instanton dominated via the response of fermions using lattice fermions with exact chiral symmetry, the overlap fermions. Considering several volumes and lattice spacings we find strong evidence for chirality of a finite density of low-lying eigenvectors of the overlap-Dirac operator in the regions where these modes are peaked. This result suggests instanton dominance of topological charge fluctuations in quenched QCD.Comment: LaTeX, 15 pages, 8 postscript figures, minor improvements, version to appear in PR

Unquenched QCD with Light Quarks

We present recent results in unquenched lattice QCD with two degenerate light sea quarks using the truncated determinant approximation (TDA). In the TDA the infrared modes contributing to the quark determinant are computed exactly up to some cutoff in quark off-shellness (typically 2$\Lambda_{QCD}$). This approach allows simulations to be performed at much lighter quark masses than possible with conventional hybrid MonteCarlo techniques. Results for the static energy and topological charge distributions are presented using a large ensemble generated on very coarse (6$^4$) but physically large lattices. Preliminary results are also reported for the static energy and meson spectrum on 10$^3$x20 lattices (lattice scale $a^{-1}$=1.15 GeV) at quark masses corresponding to pions of mass $\leq$ 200 MeV. Using multiboson simulation to compute the ultraviolet part of the quark determinant the TDA approach becomes an exact with essentially no increase in computational effort. Some preliminary results using this fully unquenched algorithm are presented.Comment: LateX, 39 pages, 16 eps figures, 1 ps figur

Microscopic universality with dynamical fermions

It has recently been demonstrated in quenched lattice simulations that the distribution of the low-lying eigenvalues of the QCD Dirac operator is universal and described by random-matrix theory. We present first evidence that this universality continues to hold in the presence of dynamical quarks. Data from a lattice simulation with gauge group SU(2) and dynamical staggered fermions are compared to the predictions of the chiral symplectic ensemble of random-matrix theory with massive dynamical quarks. Good agreement is found in this exploratory study. We also discuss implications of our results.Comment: 5 pages, 3 figures, minor modifications, to appear in Phys. Rev. D (Rapid Commun.

Small eigenvalues of the staggered Dirac operator in the adjoint representation and Random Matrix Theory

The low-lying spectrum of the Dirac operator is predicted to be universal, within three classes, depending on symmetry properties specified according to random matrix theory. The three universal classes are the orthogonal, unitary and symplectic ensemble. Lattice gauge theory with staggered fermions has verified two of the cases so far, unitary and symplectic, with staggered fermions in the fundamental representation of SU(3) and SU(2). We verify the missing case here, namely orthogonal, with staggered fermions in the adjoint representation of SU(N_c), N_c=2, 3.Comment: 3 pages, revtex, 2 postscript figure

Kinematics of Multigrid Monte Carlo

We study the kinematics of multigrid Monte Carlo algorithms by means of acceptance rates for nonlocal Metropolis update proposals. An approximation formula for acceptance rates is derived. We present a comparison of different coarse-to-fine interpolation schemes in free field theory, where the formula is exact. The predictions of the approximation formula for several interacting models are well confirmed by Monte Carlo simulations. The following rule is found: For a critical model with fundamental Hamiltonian H(phi), absence of critical slowing down can only be expected if the expansion of in terms of the shift psi contains no relevant (mass) term. We also introduce a multigrid update procedure for nonabelian lattice gauge theory and study the acceptance rates for gauge group SU(2) in four dimensions.Comment: 28 pages, 8 ps-figures, DESY 92-09

Microscopic universality in the spectrum of the lattice Dirac operator

Large ensembles of complete spectra of the Euclidean Dirac operator for staggered fermions are calculated for SU(2) lattice gauge theory. The accumulation of eigenvalues near zero is analyzed as a signal of chiral symmetry breaking and compared with parameter-free predictions from chiral random matrix theory. Excellent agreement for the distribution of the smallest eigenvalue and the microscopic spectral density is found. This provides direct evidence for the conjecture that these quantities are universal functions.Comment: 4 pages, 3 figures (included), REVTeX 3.1; updated version to appear in Phys. Rev. Let

Chiral Condensate in the Deconfined Phase of Quenched Gauge Theories

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 show that the part of the spectrum responsible for the chiral condensate can be understood as arising from a dilute gas of instantons and anti-instantons.Comment: Revtex, 16 pages, 3 postscript figure