Remnants of the index theorem on the lattice

We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD generated using a Symanzik-improved gluon action. We find a clear separation of the spectrum into would-be zero modes and others. The number of would-be zero modes depends on the topological charge as expected from the Index Theorem, and their chirality expectation value is large (≈ 0.7). The remaining modes have low chirality and show clear signs of clustering into quartets and approaching the random matrix theory predictions for all topological charge sectors. We conclude that improvement of the fermionic and gauge actions moves the staggered quarks closer to the continuum limit where they respond correctly to QCD topology.

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“…As { / D, γ ts 5 } = 0, there is no exact Index Theorem and all eigenmodes in principle contribute to Eqn. (3) [10].…”

Section: Introductionmentioning

confidence: 99%

Index Theorem and Universality Properties of the Low-Lying Eigenvalues of Improved Staggered Quarks

2004

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“…Since the quenched-theory Boltzmann weight is strictly positive and independent of m 1 , the pion two-point function indeed has a 1/m 1 divergence! Clearly, (nearly) exceptional configurations [11] -the ones responsible for the nearzero modes of H(m 0 ) -are also directly responsible for the 1/m 1 divergence. We conclude that the finite-volume, super-critical quenched theory is ill-defined for m 1 = 0, so one must keep m 1 = 0.…”

Section: Localization Mobility Edge and The Phase Diagrammentioning

confidence: 99%

“…[14]). For this purpose we may interpret H(m 0 ) as the hamiltonian of a 3 Exceptional configurations [11] -defined by the condition that H(m 0 ) has a zero mode for some m 0 -were discarded in ref. [10].…”

Section: Introductionmentioning

confidence: 99%

Localization in lattice QCD (with emphasis on practical implications)

Golterman

Shamir

2004

Nuclear Physics B - Proceedings Supplements

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When Anderson localization takes place in a quenched disordered system, a continuous symmetry can be broken spontaneously without accompanying Goldstone bosons. Elaborating on this observation we propose a unified, microscopic physical picture of the phase diagram of quenched and unquenched QCD with two flavors of Wilson fermions. The phase with Goldstone bosons-by definition the Aoki phase-is always identified as the region where the mobility edge of the (hermitian) Wilson operator is zero. We then discuss the implications for domainwall and overlap fermions. We conclude that both formulations are valid only well outside the Aoki phase of the associated Wilson-operator kernel, because this is where locality and chirality can be both maintained.

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“…Here M −1 is the inverse fermion matrix and κ p a renormalization constant [10]. Again we used improved SET to estimate the right hand side of eq.…”

Section: Topology and Setmentioning

confidence: 99%

News on disconnected diagrams

Viehoff

1999

Nuclear Physics B - Proceedings Supplements

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We present evidence for disconnected contributions to the σπN term and the flavor singlet axial coupling g 0 A of the proton on full QCD configurations, which are obtained by means of improved stochastic estimator techniques.Furthermore we discuss results from the fermionic determination of the topological charge of the QCD vacuum (in the spirit of the Athiya-Singer theorem) again achieved with stochastic estimator methods. It turns out that this approach provides an monitor for the tunneling efficiency of the HMC on QCD with dynamical Wilson fermions which is independent on the pure gluonic method that implies cooling.

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Remnants of the index theorem on the lattice

Cited by 204 publications

References 34 publications

Index Theorem and Universality Properties of the Low-Lying Eigenvalues of Improved Staggered Quarks

Index Theorem and Universality Properties of the Low-Lying Eigenvalues of Improved Staggered Quarks

Localization in lattice QCD (with emphasis on practical implications)

News on disconnected diagrams

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