arXiv subjects

A. J. van der Sijs

Publications and source records attributed to A. J. van der Sijs.

At least 19 recordsLinked to original sources

arXiv2000

Exact Solution of the Infinite-Range Quantum Mattis Model

We have solved the quantum version of the Mattis model with infinite-range interactions. A variational approach gives the exact solution for the infinite-range system, in spite of the non-commutative nature of the quantum spin components; this implies that quantum effects are not predominant in determining the macroscopic properties of the system. Nevertheless, the model has a surprisingly rich phase behaviour, exhibiting phase diagrams with tricritical, three-phase and critical end points.

cond-mat.dis-nn↗

arXiv1999

Mass protection via translational invariance

We propose a way of protecting a Dirac fermion interacting with a scalar field from acquiring a mass from the vacuum. It is obtained through an implementation of translational symmetry when the theory is formulated with a momentum cutoff, which forbids the usual Yukawa term. We consider that this mechanism can help to understand the smallness of neutrino masses without a tuning of the Yukawa coupling. The prohibition of the Yukawa term for the neutrino forbids at the same time a gauge coupling between the right-handed electron and neutrino. We prove that this mechanism can be implemented on the lattice.

hep-th↗

arXiv1999

A new mechanism of mass protection for fermions

We present a way of protecting a Dirac fermion interacting with a scalar (Higgs) field from getting a mass from the vacuum. It is obtained through an implementation of translational symmetry when the theory is formulated with a momentum cutoff, which forbids the usual Yukawa term. We consider that this mechanism can help to understand the smallness of neutrino masses without a tuning of the Yukawa coupling. The prohibition of the Yukawa term for the neutrino forbids at the same time a gauge coupling between the right-handed electron and neutrino. We prove that this mechanism can be implemented on the lattice.

hep-lat↗

arXiv1999

Phase-diagram and quasiparticles of a lattice SU(2) scalar-fermion model in (2+1) dimensions

The phase diagram at zero temperature of a lattice SU(2) scalar-fermion model in (2+1) dimensions is studied numerically and with Mean-Field methods. Special attention is devoted to the strong coupling regime. We have developed a new method to adaptate the Hybrid Monte Carlo algorithm to the O(3) non-linear $σ$ model constraint. The charged excitations in the various phases are studied at the Mean-Field lev el. Bound states of two charged fermions are found in a strongly coupled {\it paramagnetic} phase. On the other hand, in the strongly coupled antiferromagnetic phase fermionic excitations around momenta $(\pm\fracπ{2},\pm\fracπ{2},\pm\fracπ{2})$ emerge.

cond-mat↗

arXiv1998

Laplacian Abelian Projection: Abelian dominance and Monopole dominance

A comparative study of Abelian and Monopole dominance in the Laplacian and Maximally Abelian projected gauges is carried out. Clear evidence for both types of dominance is obtained for the Laplacian projection. Surprisingly, the evidence is much more ambiguous in the Maximally Abelian gauge. This is attributed to possible ``long-distance imperfections'' in the maximally abelian gauge fixing.

hep-lat↗

arXiv1998

A model for the doped copper oxide compounds

We present a relativistic spin-fermion model for the cuprates, in which both the charge and spin degrees of freedom are treated dynamically. The spin-charge coupling parameter is associated with the doping fraction. The model is able to account for the various phases of the cuprates and their properties, not only at low and intermediate doping but also for (highly) over-doped compounds. In particular, we acquire a qualitative understanding of high-T_c superconductivity through Bose-Einstein condensation of bound charge pairs. The mechanism that binds these pairs does not require a Fermi sea.

cond-mat.supr-con↗

arXiv1998

High-Tc superconductivity through a charge pairing mechanism in a strongly coupled disordered phase

We present a lattice field theory of spins coupled to Dirac fermions, as a model for the doped copper oxide compounds. Both the fermionic and spin degrees of freedom are treated dynamically. The influence of the charge carriers on the magnetic ordering follows automatically. The magnetic phase diagram at zero temperature is studied numerically and with Mean-Field methods. The Hybrid Monte Carlo algorithm is adapted to the O(3) non-linear sigma model constraint. The charged excitations in the various phases are studied at the Mean-Field level. Bound states of two charged fermions are found in a strongly coupled paramagnetic phase, without requiring a Fermi sea. We acquire a qualitative understanding of high-T$_c$ superconductivity through Bose-Einstein condensation of those dynamically bound pairs. The model also implies insulating behaviour at low doping, and Fermi liquid behaviour at large doping. We predict the possibility of reentrant superconductivity and the absence of superconductivity in spin-1 and spin-3/2 materials.

cond-mat.supr-con↗

arXiv1998

Abelian Projection without Ambiguities

Laplacian Abelian Projection is discussed. This term refers to the use of a new (``Laplacian'') gauge fixing prescription for implementing the Abelian Projection of QCD. The gauge condition is based on the lowest-lying eigenvector of the covariant Laplacian operator in the adjoint representation. This Laplacian gauge fixing procedure is free of the ambiguities which plague lattice simulations which work with the popular Maximally Abelian Gauge. Furthermore, Laplacian gauge fixed configurations enjoy a natural kind of smoothness. These two properties are crucial for a reliable determination of physical quantities using the Abelian Projection. We also examine a new, Higgs-field-like observable which emerges as a by-product of the method. This quantity can be used to identify magnetic monopoles in a way independent of the traditional prescription. It is argued that physically relevant magnetic monopoles are accomodated well by the Laplacian method, while they are suppressed (too) strongly in Maximally Abelian Gauge. Finally, first evidence of abelian dominance in the Laplacian Abelian Projection is presented.

hep-lat↗

arXiv1997

Three topics in the Schwinger model

1. We compare Monte Carlo results with analytic predictions for the fermion condensate, in the massive one-flavour Schwinger model. 2. We illustrate on the Schwinger model how to facilitate transitions between topological sectors by a simple reweighting method. 3. We discuss exact, non-perturbative improvement of the gauge sector.

hep-lat↗

arXiv1997

A lattice field theoretical model for high-$T_c$ superconductivity

We present a 2+1-dimensional lattice model for the copper oxide superconductors and their parent compounds, in which both the charge and spin degrees of freedom are treated dynamically. The spin-charge coupling parameter is associated to the doping fraction in the cuprates. The model is able to account for the various phases of the cuprates and their properties, not only at low and intermediate doping but also for (highly) over-doped compounds. We acquire a qualitative understanding of high-$T_c$ superconductivity as a Bose-Einstein condensation of bound charge pairs.

hep-lat↗

arXiv1996

Laplacian Abelian Projection

A new partial gauge fixing condition for the abelian projection is introduced. It is based on the lowest-lying eigenvector of a covariant Laplacian operator. This gauge is smooth and free of lattice Gribov copies. These properties are important for an unambiguous computation of the abelian projected gauge field configuration.

hep-lat↗

arXiv1996

Monte-Carlo study of the $Δρ$ parameter

We present results concerning a lattice study of the electroweak $ρ$-parameter. We have used an SU(2)$\times$U(1) symmetric chiral Yukawa model built with Zaragoza fermions. The decoupling of the species doublers in this model is verified numerically. We find that the numerical data for $Δρ$ are well described by one-loop perturbation theory with the same finite volume and with the same finite cut-off. However, a finite cut-off can cause substantial deviations of $Δρ$ from the standard value, even in infinite volume.

hep-lat↗

arXiv1995

A class of chiral fermion models

We study the relation between the Roma and Zaragoza proposals for chiral fermions on the lattice. The fermion action in the Roma approach is shown to be equivalent to one of the Zaragoza type. This result is used to perform a mean-field study of the phase diagram for chiral Yukawa models based on the Roma action. The phase diagram is compared with the one based on the Zaragoza model with the most local choice for the fermion interactions.

hep-lat↗

arXiv1995

Delta-rho in an SU(2) X U(1) chiral Yukawa model

We report on a simulation in progress of an SU(2) X U(1) fermion-Higgs model with two *non-degenerate* fermion doublets. The Zaragoza proposal for chiral lattice fermions is used; naive fermions are studied for comparison. The aims of this simulation are a non-perturbative study of the decoupling of species doublers, of triviality bounds on the Higgs and fermion masses and of the phenomenological quantity Delta-rho.

hep-lat↗

arXiv1995

RTNN: The new parallel machine in Zaragoza

I report on the development of RTNN, a parallel computer designed as a 4^4 hypercube of 256 T9000 transputer nodes, each with 8 MB memory. The peak performance of the machine is expected to be 2.5 Gflops.

hep-lat↗

arXiv1995

Some views on monopoles and confinement

Aspects of the monopole condensation picture of confinement are discussed. First, the nature of the monopole singularities in the abelian projection approach is analysed. Their apparent gauge dependence is shown to have a natural interpretation in terms of 't~Hooft-Polyakov-like monopoles in euclidean SU(2) gauge theory. Next, the results and predictions of a realization of confinement through condensation of such monopoles are summarized and compared with numerical data.

hep-th↗

arXiv1995

On ferrimagnetic phases in chiral Yukawa models

We discuss the phase structure of chiral Yukawa models in the mean-field approximation. In particular, we examine under which conditions a ferrimagnetic phase appears, by calculating the slopes of possible second order phase transition lines near a critical point. Our results contrast with some statements which appeared in the literature recently.

hep-lat↗

arXiv1994

Roma versus Zaragoza

The Roma and Zaragoza actions for chiral fermions on the lattice are shown to be essentially equivalent. The auxiliary fermion fields in the Roma model can be integrated out, and the resulting action is a special case of the Zaragoza approach. We use this result to perform a mean-field study of the phase diagram of chiral Yukawa models in the Roma formulation.

hep-lat↗