Truncated overlap fermions

Boriçi, Artan

doi:10.1016/s0920-5632(00)91802-4

Cited by 62 publications

(90 citation statements)

References 12 publications

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“…Both quenched [17,[19][20][21][22][23][24][25][26][27][28][29][30][31] and dynamical [31][32][33][34][35]12] domain wall fermion simulations have been conducted and the domain wall approach is readily adapted to current algorithms for lattice QCD. (Much work is also being done on the numerical implementation of the overlap formulation and its variations [36][37][38][39][40][41][42][43][44][45][46].) A fundamental question, which is a major part of this paper, involves quantifying the residual chiral symmetry breaking effects of finite extent in the fifth dimension.…”

Section: Introductionmentioning

confidence: 99%

Quenched lattice QCD with domain wall fermions and the chiral limit

et al. 2004

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Quenched QCD simulations on three volumes, 8 3 ×, 12 3 × and 16 3 × 32 and three couplings, β = 5.7, 5.85 and 6.0 using domain wall fermions provide a consistent picture of quenched QCD. We demonstrate that the small induced effects of chiral symmetry breaking inherent in this formulation can be described by a residual mass (m res ) whose size decreases as the separation between the domain walls (L s ) is increased. However, at stronger couplings much larger values of L s are required to achieve a given physical value of m res . For β = 6.0 and L s = 16, we find m res /m s = 0.033(3), while for β = 5.7, and L s = 48, m res /m s = 0.074(5), where m s is the strange quark mass. These values are significantly smaller than those obtained from a more naive determination in our earlier studies. Important effects of topological near zero modes which should afflict an accurate quenched calculation are easily visible in both the chiral condensate and the pion propagator. These effects can be controlled by working at an appropriately large volume. A non-linear behavior of m 2 π in the limit of small quark mass suggests the presence of additional infrared subtlety in the quenched approximation. Good scaling is seen both in masses and in f π over our entire range, with inverse lattice spacing varying between 1 and 2 GeV.

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Section: Introductionmentioning

confidence: 99%

Quenched lattice QCD with domain wall fermions and the chiral limit

et al. 2004

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“…Still the five-dimensional point of view would be useful to get insights into the problem we face (cf. [58,59]). …”

Section: Resultsmentioning

confidence: 99%

Analytic progress on exact lattice chiral symmetry

Kikukawa

2002

Nuclear Physics B - Proceedings Supplements

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Theoretical issues of exact chiral symmetry on the lattice are discussed and related recent works are reviewed. For chiral theories, the construction with exact gauge invariance is reconsidered from the point of view of domain wall fermion. The issue in the construction of electroweak theory is also discussed. For vector-like theories, we discuss unitarity (positivity), Hamiltonian approach, and several generalizations of the Ginsparg-Wilson relation (algebraic and odd-dimensional).

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“…The two forms are equivalent in the limit of infinite fifth dimension [44,45]. Yet another form is the perfect action [46], so named because it is defined as the fixed point of a block spin transformation of renormalization group for QCD.…”

Section: Lattice Fermion Action With Chiral Symmetrymentioning

confidence: 99%

Kenneth Wilson and Lattice QCD

Ukawa

2015

J Stat Phys

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We discuss the physics and computation of lattice QCD, a spacetime lattice formulation of quantum chromodynamics, and Kenneth Wilson's seminal role in its development. We start with the fundamental issue of confinement of quarks in the theory of the strong interactions, and discuss how lattice QCD provides a framework for understanding this phenomenon. A conceptual issue with lattice QCD is a conflict of space-time lattice with chiral symmetry of quarks. We discuss how this problem is resolved. Since lattice QCD is a non-linear quantum dynamical system with infinite degrees of freedom, quantities which are analytically calculable are limited. On the other hand, it provides an ideal case of massively parallel numerical computations. We review the long and distinguished history of parallel-architecture supercomputers designed and built for lattice QCD. We discuss algorithmic developments, in particular the difficulties posed by the fermionic nature of quarks, and their resolution. The triad of efforts toward better understanding of physics, better algorithms, and more powerful supercomputers have produced major breakthroughs in our understanding of the strong interactions. We review the salient results of this effort in understanding the hadron spectrum, the Cabibbo-Kobayashi-Maskawa matrix elements and CP violation, and quark-gluon plasma at high temperatures. We conclude with a brief summary and a future perspective.

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Truncated overlap fermions

Abstract: In this talk I propose a new computational scheme with overlap fermions and a fast algorithm to invert the corresponding Dirac operator.

Cited by 62 publications

References 12 publications

Quenched lattice QCD with domain wall fermions and the chiral limit

Quenched lattice QCD with domain wall fermions and the chiral limit

Analytic progress on exact lattice chiral symmetry

Kenneth Wilson and Lattice QCD

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