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Ivan Horvath

Publications and source records attributed to Ivan Horvath.

32 records · Page 2Linked to original sources
arXiv2000

Strong Non-Ultralocality of Ginsparg-Wilson Fermionic Actions

It is shown that it is impossible to construct a free theory of fermions on infinite hypercubic Euclidean lattice in even number of dimensions that: (a) is ultralocal, (b) respects the symmetries of hypercubic lattice, (c) chirally nonsymmetric part of its propagator is local, and (d) describes single species of massless Dirac fermions in the continuum limit. This establishes non-ultralocality for arbitrary doubler-free Ginsparg-Wilson fermionic action with hypercubic symmetries ("strong non-ultralocality"), and complements the earlier general result on non-ultralocality of infinitesimal Ginsparg-Wilson-Luscher symmetry transformations ("weak non-ultralocality").

hep-lat↗
arXiv2000

Comment on hep-lat/9901005 v1-v3 by W. Bietenholz

I comment on the above paper(s) discussing the issue of non-ultralocality for Ginsparg-Wilson fermionic actions. The purpose of this note is to point out that the new claim in "v3" (Feb 24, 2000), alleging the proof for "all Ginsparg-Wilson fermions", might not be substantiated. The remarkable evolution of versions of this paper is put in context with the literature existing at the time of their appearance.

hep-lat↗
arXiv1999

Stochastic Split Determinant Algorithms

I propose a large class of stochastic Markov processes associated with probability distributions analogous to that of lattice gauge theory with dynamical fermions. The construction incorporates the idea of approximate spectral split of the determinant through local loop action, and the idea of treating the infrared part of the split through explicit diagonalizations. I suggest that exact algorithms of practical relevance might be based on the Markov processes so constructed.

hep-lat↗
arXiv1999

Ginsparg-Wilson-Luscher Symmetry and Ultralocality

Important recent discoveries suggest that Ginsparg-Wilson-Luscher (GWL) symmetry has analogous dynamical consequences for the theory on the lattice as chiral symmetry does in the continuum. While it is well known that inherent property of lattice chiral symmetry is fermion doubling, we show here that inherent property of GWL symmetry is that the infinitesimal symmetry transformation couples fermionic degrees of freedom at arbitrarily large lattice distances (non-ultralocality). The consequences of this result for ultralocality of symmetric actions are discussed.

hep-lat↗
arXiv1998

Ginsparg-Wilson Relation and Spin Chains

The Baxter 8-vertex model is equivalent to a particular lattice formulation of a self-interacting, massive Dirac fermion theory. In the time-continuum limit, the lattice Hamiltonian (XYZ spin chain) can be explicitly transformed to a lattice Dirac Hamiltonian. We show that the kernel describing the quadratic part of this Hamiltonian satisfies a one-dimensional version of the Ginsparg-Wilson relation. The corresponding conserved charge is derived and compared with the conserved arrow number of the 8-vertex model.

hep-lat↗
arXiv1998

Ginsparg-Wilson Relation and Ultralocality

It is shown that it is impossible to construct a free theory of fermions on infinite hypercubic Euclidean lattice in four dimensions that is: (a) ultralocal, (b) respects symmetries of hypercubic lattice, (c) corresponding kernel satisfies D gamma5 + gamma5 D = D gamma5 D (Ginsparg-Wilson relation), (d) describes single species of massless Dirac fermions in the continuum limit.

hep-lat↗
arXiv1997

The LHMC Algorithm for Free Field Theory: Reexamining Overrelaxation

We analyze the autocorrelations for the LHMC algorithm in the context of free field theory. In this case this is just Adler's overrelaxation algorithm. We consider the algorithm with even/odd, lexicographic, and random updates, and show that its efficiency depends crucially on this ordering of sites when optimized for a given class of operators. In particular, we show that, contrary to previous expectations, it is possible to eliminate critical slowing down (z[int]=0) for a class of interesting observables, including the magnetic susceptibility: this can be done with lexicographic updates but is not possible with even/odd (z[int]=1) or random (z[int]=2) updates. We are considering the dynamical critical exponent z[int] for integrated autocorrelations rather than for the exponential autocorrelation time; this is reasonable because it is the integrated autocorrelation which determines the cost of a Monte Carlo computation.

hep-lat↗
arXiv1996

Non-Reversibility of Molecular Dynamics Trajectories

We study the non-reversibility of molecular dynamics trajectories arising from the amplification of rounding errors. We analyse the causes of such behaviour and give arguments, indicating that this does not pose a significant problem for Hybrid Monte Carlo computations. We present data for pure SU(3) gauge theory and for QCD with dynamical fermions on small lattices to illustrate and to support some of our ideas.

hep-lat↗
arXiv1995

The Phase Structure of the Schwinger Model on the Lattice with Wilson Fermions in the Hartree-Fock Approximation

The phase diagram of the Schwinger model on the lattice with one and two degenerate flavours of Wilson fermions is investigated in the Hartree-Fock approximation. In case of a single flavour (not directly amenable to numerical simulation), the calculation indicates the existence of the parity violating phase at both weak and intermediate-to-strong couplings. In the broken phase, the Hartree-Fock vacuum sustains a nonzero electric field. With two flavours, parity is not broken at weak coupling. However, both parity and flavour become spontaneously broken at the Hartree-Fock level as the coupling becomes strong.

hep-lat↗
arXiv1995

Surface modes and parity violation in Schwinger model on the lattice

The phase diagram of the Schwinger model on the lattice with Wilson fermions is investigated in the Hartree-Fock approximation. In case of single flavour (not directly amenable to simulations), the calculation indicates the existence of the parity violating phase at both weak and intermediate-to-strong couplings. Hartree-Fock vacuum sustains a nonzero electric field in this broken phase. The phase structure of the model with two flavours is also discussed.

hep-lat↗
arXiv1994

Surface states and chiral symmetry on the lattice

In a Hamiltonian formalism we study chiral symmetry for lattice Fermions formulated in terms of Shockley surface states bound to a wall in an extra spatial dimension. For hadronic physics this provides a natural scheme for taking quark masses to zero without requiring a precise tuning of parameters. We illustrate the chiral anomaly as a flow of states in this extra dimension. We discuss two alternatives for extending the picture to a chiral coupling of gauge fields to such Fermions; one with a small explicit breaking of gauge symmetry and one one with heavy mirror Fermions.

hep-lat↗
arXiv1993

Surface modes and chiral symmetry (Wilson Fermions in a box)

We give a Hamiltonian discussion of surface states in an extra dimension as a basis for chiral fermions in lattice models. Such modes appear with the Wilson fermion action when the hopping parameter exceeds a critical value. The association of such states with the closing and reopening of a band gap was noted by Shockley in 1939. Poster presented by Michael Creutz at Lattice 93. Uuencoded compressed postscript file.

hep-lat↗