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C. B. Lang

Publications and source records attributed to C. B. Lang.

At least 127 records · Page 7Linked to original sources
arXiv1999

Comparing lattice Dirac operators with Random Matrix Theory

We study the eigenvalue spectrum of different lattice Dirac operators (staggered, fixed point, overlap) and discuss their dependence on the topological sectors. Although the model is 2D (the Schwinger model with massless fermions) our observations indicate possible problems in 4D applications. In particular misidentification of the smallest eigenvalues due to non-identification of the topological sector may hinder successful comparison with Random Matrix Theory (RMT).

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arXiv1999

Eigenvalue spectrum of massless Dirac operators on the lattice

We present a detailed study of the interplay between chiral symmetry and spectral properties of the Dirac operator in lattice gauge theories. We consider, in the framework of the Schwinger model, the fixed point action and a fermion action recently proposed by Neuberger. Both actions show the remnant of chiral symmetry on the lattice as formulated in the Ginsparg-Wilson relation. We check this issue for practical implementations, also evaluating the fermion condensate in a finite volume by a subtraction procedure. Moreover, we investigate the distribution of the eigenvalues of a properly defined anti-hermitian lattice Dirac operator, studying the statistical properties at the low lying edge of the spectrum. The comparison with the predictions of chiral Random Matrix Theory enables us to obtain an estimate of the infinite volume fermion condensate.

hep-lat↗
arXiv1998

Fixed point action for the massless lattice Schwinger model

We determine non-perturbatively the fixed-point action for fermions in the two-dimensional U(1) gauge (Schwinger) model. This is done by iterating a block spin transformation in the background of non-compact gauge field configurations sampled according to the (perfect) Gaussian measure. The resulting action has 123 independent couplings, is bilinear in the Grassmann fields, gauge-invariant by considered the compact gauge transporters and localized within a $7\times 7$ lattice centered around one of the fermions. We then simulate the model at various values of $β$ and compare with results obtained with the Wilson fermion action. We find excellent improvement for the studied observables (propagators and masses).

hep-lat↗
arXiv1998

SW action for the lattice Schwinger model

We study some aspects of the ${\cal O}(a)$ improved Sheikholeslami-Wohlert (SW) action for the lattice Schwinger model. We find some improvement concerning the distribution of eigenvalues of the Dirac operator and of the masses but little or no improvement for rotational invariance of correlators or dispersion relations.

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arXiv1998

Spectrum of the fixed point Dirac operator in the Schwinger model

Recently, properties of the fixed point action for fermion theories have been pointed out indicating realization of chiral symmetry on the lattice. We check these properties by numerical analysis of the spectrum of a parametrized fixed point Dirac operator investigating also microscopic fluctuations and fermion condensation.

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arXiv1998

Wilson, fixed point and Neuberger's lattice Dirac operator for the Schwinger model

We perform a comparison between different lattice regularizations of the Dirac operator for massless fermions in the framework of the single and two flavor Schwinger model. We consider a) the Wilson-Dirac operator at the critical value of the hopping parameter; b) Neuberger's overlap operator; c) the fixed point operator. We test chiral properties of the spectrum, dispersion relations and rotational invariance of the mesonic bound state propagators.

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arXiv1998

The lattice Schwinger model with the SW action

We perform a model study on the 2-flavor lattice Schwinger model using standard Wilson and ${\cal O}(a)$ improved Sheikholeslami-Wohlert (SW) action. We find, that the phase diagram is altered, the critical line shifted closer towards its continuum value $κ_c=0.25$. We find no improvement in the rotation invariance of meson propagators; the scaling of the Schwinger mass is considerably improved, high momentum states are not. The additional cost of $\approx 30 %$ CPU-time is highly justified when calculating masses, but not for high momentum observables.

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arXiv1998

Chiral properties of the fixed point action of the Schwinger model

We study the spectrum properties for a recently constructed fixed point lattice Dirac operator. We also consider the problem of the extraction of the fermion condensate, both by direct computation, and through the Banks-Casher formula by analyzing the density of eigenvalues of a redefined antihermitean lattice Dirac operator.

hep-lat↗
arXiv1997

Scaling of gauge balls and static potential in the confinement phase of the pure U(1) lattice gauge theory

We investigate the scaling behaviour of gauge-ball masses and static potential in the pure U(1) lattice gauge theory on toroidal lattices. An extended gauge field action $-\sum_P(β\cosΘ_P + γ\cos2Θ_P)$ is used with $γ= -0.2$ and -0.5. Gauge-ball correlation functions with all possible lattice quantum numbers are calculated. Most gauge-ball masses scale with the non-Gaussian exponent $ν_{ng}\approx 0.36$. The $A_1^{++}$ gauge-ball mass scales with the Gaussian value $ν_{g} \approx 0.5$ in the investigated range of correlation lengths. The static potential is examined with Sommer's method. The long range part scales consistently with $ν_{ng}$ but the short range part tends to yield smaller values of $ν$. The $β$-function, having a UV stable zero, is obtained from the running coupling. These results hold for both $γ$ values, supporting universality. Consequences for the continuum limit of the theory are discussed.

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arXiv1997

Chiral symmetry in the 2-flavour lattice Schwinger model

We study the 2-flavour lattice Schwinger model: QED in D=2 with two fermion species of identical mass. In the simulation we are using Wilson fermions where chiral symmetry is explicitly broken. Since there is no known simple order parameter it is non-trivial to identify the critical line of the chiral phase transition. We therefore need to find observables which allow an identification of a possible restoration of chiral symmetry. We utilize the PCAC-relations in order to identify the critical coupling, where chiral symmetry is restored.

hep-lat↗
arXiv1997

A fixed-point action for the lattice Schwinger model

We determine non-perturbatively a fixed-point (FP) action for fermions in the two-dimensional U(1) gauge (Schwinger) model. Our parameterization for the fermionic action has terms within a $7\times 7$ square on the lattice, using compact link variables. With the Wilson fermion action as starting point we determine the FP-action by iterating a block spin transformation (BST) with a blocking factor of 2 in the background of non-compact gauge field configurations sampled according to the (perfect) Gaussian measure. We simulate the model at various values of $β$ and find excellent improvement for the studied observables.

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arXiv1997

Topological Charge and the Spectrum of the Fermion Matrix in Lattice-QED_2

We investigate the interplay between topological charge and the spectrum of the fermion matrix in lattice-QED_2 using analytic methods and Monte Carlo simulations with dynamical fermions. A new theorem on the spectral decomposition of the fermion matrix establishes that its real eigenvalues (and corresponding eigenvectors) play a role similar to the zero eigenvalues (zero modes) of the Dirac operator in continuous background fields. Using numerical techniques we concentrate on studying the real part of the spectrum. These results provide new insights into the behaviour of physical quantities as a function of the topological charge. In particular we discuss fermion determinant, effective action and pseudoscalar densities.

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arXiv1997

Quantum Fluctuations versus Topology - a Study in U(1)_2 Lattice Gauge Theory

Using the geometric definition of the topological charge we decompose the path integral of 2-dimensional U(1) lattice gauge theory into topological sectors. In a Monte Carlo simulation we compute the average value of the action as well as the distribution of its values for each sector separately. These numbers are compared with analytic lower bounds of the action which are relevant for classical configurations carrying topological charge. We find that quantum fluctuations entirely dominate the path integral. Our results for the probability distribution of the Monte Carlo generated configurations among the topological sectors can be understood by a semi-phenomenological argument.

hep-lat↗
arXiv1997

Strongly coupled compact lattice QED with staggered fermions

We explore the compact U(1) lattice gauge theory with staggered fermions and gauge field action -\sum_P [β\cos(Θ_P) + γ\cos(2Θ_P)], both for dynamical fermions and in the quenched approximation. (Θ_P denotes the plaquette angle.) In simulations with dynamical fermions at various γ\le -0.2 on 6^4 lattices we find the energy gap at the phase transition of a size comparable to the pure gauge theory for γ\le 0 on the same lattice, diminishing with decreasing γ. This suggests a second order transition in the thermodynamic limit of the theory with fermions for γbelow some finite negative value. Studying the theory on large lattices at γ= -0.2 in the quenched approximation by means of the equation of state we find non-Gaussian values of the critical exponents associated with the chiral condensate, β\simeq 0.32 and δ\simeq 1.8, and determine the scaling function. Furthermore, we evaluate the meson spectrum and study the PCAC relation.

hep-lat↗
arXiv1997

Gauge-ball spectrum of the four-dimensional pure U(1) gauge theory

We investigate the continuum limit of the gauge-ball spectrum in the four-dimensional pure U(1) lattice gauge theory. In the confinement phase we identify various states scaling with the correlation length exponent $ν\simeq 0.35$. The square root of the string tension also scales with this exponent, which agrees with the non-Gaussian fixed point exponent recently found in the finite size studies of this theory. Possible scenarios for constructing a non-Gaussian continuum theory with the observed gauge-ball spectrum are discussed. The $0^{++}$ state, however, scales with a Gaussian value $ν\simeq 0.5$. This suggests the existence of a second, Gaussian continuum limit in the confinement phase and also the presence of a light or possibly massless scalar in the non-Gaussian continuum theory. In the Coulomb phase we find evidence for a few gauge-balls, being resonances in multi-photon channels; they seem to approach the continuum limit with as yet unknown critical exponents. The maximal value of the renormalized coupling in this phase is determined and its universality confirmed.

hep-lat↗
arXiv1996

Properties of the non-Gaussian fixed point in 4D compact U(1) lattice gauge theory

We examine selected properties of the gauge-ball spectrum and fermionic variables in the vicinity of the recently discussed non-Gaussian fixed point of 4D compact U(1) lattice gauge theory within the quenched approximation. Approaching the critical point from within the confinement phase, our data support scaling of $T1^{+-}$ gauge-ball states in units of the string tension square root. The analysis of the chiral condensate within the framework of a scaling form for the equation of state suggests non mean-field values for the magnetic exponents $δ$ and $β_{exp}$.

hep-lat↗
arXiv1996

U(1) Gauge Theory with Villain Action on Spherical Lattices

We have studied the U(1) gauge field theory with Villain (periodic Gaussian) action on spherelike lattices. The effective size of the systems studied ranges from 6 to 16. We do not observe any 2-state signal in the distribution function of the plaquette expectation value at the deconfining phase transition. The observed finite-size scaling behavior is consistent with a second order phase transition. The obtained value of the critical exponent is nu =0.366(12) and thus neither Gaussian (nu = 0.5) nor discontinuous (nu=0.25) type, indicating a nontrivial continuum limit.

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