Uwe-Jens Wiese

Perfect lattice actions for quarks and gluons

Abstract We use perturbation theory to construct perfect lattice actions for quarks and gluons. The renormalized trajectory for free massive quarks is identified by blocking directly from the continuum. We tune a parameter in the renormalization group transformation such that for 1d configurations the perfect action reduces to the nearest-neighbor Wilson fermion action. The fixed point action for free gluons is also obtained by blocking from the continuum. For 2d configurations it reduces to the standard plaquette action. Classically perfect quark and gluon fields, quark-gluon composite operators and vector and axial vector currents are constructed as well. Also the quark-antiquark potential is derived from the classically perfect Polyakov loop. The quark-gluon and three-gluon perfect vertex functions are determined to leading order in the gauge coupling. This work provides a basis for the numerical construction of a lattice action for QCD, which is (approximately) perfect even beyond perturbation theory.

Exceptional confinement in G(2) gauge theory

The Z Z(N) center symmetry plays an important role in the deconfine-ment phase transition of SU(N) Yang-Mills theory at finite temperature. The exceptional group G(2) is the smallest simply connected gauge group with a trivial center. Hence, there is no symmetry reason why the low-and high-temperature regimes in G(2) Yang-Mills theory should be separated by a phase transition. Still, we present numerical evidence for the presence of a first order deconfinement phase transition at finite temperature. Via the Higgs mechanism, G(2) breaks to its SU(3) subgroup when a scalar field in the fundamental {7} representation acquires a vacuum expectation value v. Varying v we investigate how the G(2) deconfinement transition is related to the one in SU(3) Yang-Mills theory. Interestingly, the two transitions seem to be disconnected. We also discuss a potential dynamical mechanism that may explain this behavior.

Meron-Cluster Solution of Fermion Sign Problems

We present a general strategy to solve the notorious fermion sign problem using cluster algorithms. The method applies to various systems in the Hubbard model family as well as to relativistic fermions. Here it is illustrated for nonrelativistic lattice fermions. A configuration of fermion world lines is decomposed into clusters that contribute independently to the fermion permutation sign. A cluster whose flip changes the sign is referred to as a meron. Configurations containing meron clusters contribute 0 to the path integral, while all other configurations contribute 1 . The cluster representation describes the partition function as a gas of clusters in the zero-meron sector. {copyright} {ital 1999} {ital The American Physical Society}

Quantum link models: A discrete approach to gauge theories☆

We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as quantum spin models are related to ordinary classical spin systems. Here U(1) and SU (2) quantum link models are constructed explicitly. As Hamiltonian theories quantum link models are non-relativistic gauge theories with potential applications in condensed matter physics. When formulated with a fifth Euclidean dimension, universality arguments suggest that dimensional reduction to four dimensions occurs. Hence, quantum link models are also reformulations of ordinary quantum field theories and are applicable to particle physics, for example to QCD. The configuration space of quantum link models is discrete and hence their numerical treatment should be simpler than that of ordinary lattice gauge theories with a continuous configuration space.

Atomic quantum simulation of U(N) and SU(N) non-Abelian lattice gauge theories.

Using ultracold alkaline-earth atoms in optical lattices, we construct a quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD, including chiral symmetry breaking and restoration at nonzero temperature or baryon density. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can address the corresponding chiral dynamics in real time.

Meron-cluster simulation of the theta vacuum in the 2D O(3) model.

The 2D O(3) model with a {theta} vacuum term is formulated in terms of Wolff clusters. Each cluster carries an integer or half-integer topological charge. The clusters with charge {plus_minus}1/2 are identified as merons. At {theta}={pi} the merons are bound in pairs inducing a second order phase transition at which the mass gap vanishes. The construction of an improved estimator for the topological charge distribution makes numerical simulations of the phase transition feasible. The measured critical exponents agree with those of the {ital k}=1 Wess-Zumino-Novikov-Witten (WZNW) model. Our results are consistent with Haldane{close_quote}s conjecture fro 1D antiferromagnetic quantum spin chains. {copyright} {ital 1995 The American Physical Society.}

A determination of the low energy parameters of the 2-d Heisenberg antiferromagnet

We perform numerical simulations of the 2-d Heisenberg antiferromagnet using a cluster algorithm. Comparing the size and temperature effects of various quantities with results from chiral perturbation theory we determine the low energy parameters of the system very precisely. We finde0=−0.6693(1)J/a2 for the ground state energy density, ℳs = 0.3074(4)/a2 for the staggered magnetization,ħc=1.68(1)J a for the spin wave velocity andps=0.186(4)J for the spin stiffness. Our results agree with experimental data for the precursor insulators of high-Tc superconductors.

Monte carlo study of correlations in quantum spin ladders

We study antiferromagnetic spin-1/2 Heisenberg ladders, comprised of {ital n}{sub {ital c}} chains (2{le}{ital n}{sub {ital c}}{le}6) with ratio {ital J}{sub {perpendicular}}/{ital J}{sub {parallel}} of interchain to intrachain couplings. The correlation length {xi}({ital T}) is deduced from measurements of the correlation function. For even {ital n}{sub {ital c}}, the static structure factor exhibits a peak at a temperature below the corresponding spin gap. Results for isotropically coupled ladders ({ital J}{sub {perpendicular}}/{ital J}{sub {parallel}}=1) are compared to those for the single chain and the square lattice. For {ital J}{sub {perpendicular}}/{ital J}{sub {parallel}}{le}0.5, the correlation function of the two-chain ladder is in excellent agreement with analytic results from conformal field theory, and {xi}({ital T}) exhibits simple scaling behavior. {copyright} {ital 1996 The American Physical Society.}

Square-Lattice Heisenberg Antiferromagnet at Very Large Correlation Lengths

The correlation length of the square-lattice spin-1/2 Heisenberg antiferromagnet is studied in the low-temperature (asymptotic-scaling) regime. Our novel approach combines a very efficient loop cluster algorithm{emdash}operating directly in the Euclidean time continuum{emdash}with finite-size scaling. This enables us to probe correlation lengths up to {xi}{approx}350,000 lattice spacings, more than 3 orders of magnitude larger than in any previous study. We resolve a conundrum concerning the applicability of asymptotic-scaling formulas to experimentally and numerically determined correlation lengths. Our results have direct implications for the zero-temperature behavior of spin-1/2 ladders. {copyright} {ital 1998} {ital The American Physical Society}

Monopole condensate and monopole mass in U(1) lattice gauge theory

Abstract The monopole condensate in the confined phase and the monopole mass in the Coulomb phase of U(1) lattice gauge theory are computed in numerical simulations using a monopole correlation function introduced by Frohlich and Marchetti. The finite-size effects of (magnetically) charged particles in periodic and antiperiodic volumes are discussed in detail and their relation to the infraparticle problem is investigated. By duality the results also apply to the noncompact abelian Higgs model.