The Möbius domain wall fermion algorithm Brower, Richard C.; Neff, Harmut; Orginos, Kostas
Computer physics communications,
11/2017, Letnik:
220, Številka:
C
Journal Article
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We present a review of the properties of generalized domain wall Fermions, based on a (real) Möbius transformation on the Wilson overlap kernel, discussing their algorithmic efficiency, the degree of ...explicit chiral violations measured by the residual mass (mres) and the Ward–Takahashi identities. The Möbius class interpolates between Shamir’s domain wall operator and Boriçi’s domain wall implementation of Neuberger’s overlap operator without increasing the number of Dirac applications per conjugate gradient iteration. A new scaling parameter (α) reduces chiral violations at finite fifth dimension (Ls) but yields exactly the same overlap action in the limit Ls→∞. Through the use of 4d Red/Black preconditioning and optimal tuning for the scaling α(Ls), we show that chiral symmetry violations are typically reduced by an order of magnitude at fixed Ls. We argue that the residual mass for a tuned Möbius algorithm with α=O(1∕Lsγ) for γ<1 will eventually fall asymptotically as mres=O(1∕Ls1+γ) in the case of a 5D Hamiltonian with out a spectral gap.
Holographic conformal field theories (CFTs) are usually studied in a limit where the gravity description is weakly coupled. By contrast, lattice quantum field theory can be used as a tool for doing ...computations in a wider class of holographic CFTs where nongravitational interactions in AdS become strong, and gravity is decoupled. We take preliminary steps for studying such theories on the lattice by constructing the discretized theory of a scalar field in AdS2 and investigating its approach to the continuum limit in the free and perturbative regimes. Our main focus is on finite sublattices of maximally symmetric tilings of hyperbolic space. Up to boundary effects, these tilings preserve the triangle group as a large discrete subgroup of AdS2, but have a minimum lattice spacing that is comparable to the radius of curvature of the underlying spacetime. We quantify the effects of the lattice spacing as well as the boundary effects, and find that they can be accurately modeled by modifications within the framework of the continuum limit description. We also show how to do refinements of the lattice that shrink the lattice spacing at the cost of breaking the triangle group symmetry of the maximally symmetric tilings.
Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a ...multigrid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the Kähler-Dirac spin structure prior to the Galerkin projection. We present numerical results for the two-dimensional, two-flavor Schwinger model; however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.
The phenomena of critical slowing down in the iterative solution of the Dirac equation presents a major challenge to further applications of lattice field theory in the approach to the continuum ...solution. We propose a new multigrid approach for chiral fermions, applicable to both the 5D domain wall or 4D overlap operator. The central idea is to directly coarsen the 4D Wilson kernel, giving an effective domain wall or overlap operator on each level. We provide here an explicit construction for the Shamir domain wall formulation with numerical tests for the 2D Schwinger prototype, demonstrating near ideal multigrid scaling. The framework is designed for a natural extension to 4D lattice QCD chiral fermions, such as the Möbius, Zolotarev or Borici domain wall discretizations or directly to a rational expansion of the 4D overlap operator. For the Shamir operator, the effective overlap operator is isolated by the use of a Pauli-Villars preconditioner in the spirit of the Kähler-Dirac spectral map used in a recent staggered multigrid algorithm R. C. Brower, E. Weinberg, M. A. Clark, and A. Strelchenko, Phys. Rev. D 97, 114513 (2018).
The lattice Dirac equation is formulated on a simplicial complex which approximates a smooth Riemann manifold by introducing a lattice vierbein on each site and a lattice spin connection on each ...link. Care is taken so the construction applies to any smooth D-dimensional Riemannian manifold that permits a spin connection. It is tested numerically in 2D for the projective sphere S2 in the limit of an increasingly refined sequence of triangles. The eigenspectrum and eigenvectors are shown to converge rapidly to the exact result in the continuum limit. In addition comparison is made with the continuum Ising conformal field theory on S2. Convergence is tested for the two point, ⟨ε(x1)ε(x2)⟩, and the four point, ⟨σ(x1)ε(x2)ε(x3)σ(x4)⟩, correlators for the energy, ε(x)=iψ¯(x)ψ(x), and twist operators, σ(x), respectively.
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This document is one of a series of white papers from the USQCD Collaboration. Here, we discuss opportunities for lattice field theory research to make an impact on models of new physics beyond the ...Standard Model, including composite Higgs, composite dark matter, and supersymmetric theories.
Composite Higgs models must exhibit very different dynamics from quantum chromodynamics (QCD) regardless whether they describe the Higgs boson as a dilatonlike state or a pseudo-Nambu-Goldstone ...boson. Large separation of scales and large anomalous dimensions are frequently desired by phenomenological models. Mass-split systems are well-suited for composite Higgs models because they are governed by a conformal fixed point in the ultraviolet but are chirally broken in the infrared. In this work we use lattice field theory calculations with domain wall fermions to investigate a system with four light and six heavy flavors. We demonstrate how a nearby conformal fixed point affects the properties of the four light flavors that exhibit chiral symmetry breaking in the infrared. Specifically we describe hyperscaling of dimensionful physical quantities and determine the corresponding anomalous mass dimension. We obtain ym = 1 + γ∗ = 1.47(5) suggesting that Nf = 10 lies inside the conformal window. Comparing the low energy spectrum to predictions of dilaton chiral perturbation theory, we observe excellent agreement which supports the expectation that the 4 + 6 mass-split system exhibits near-conformal dynamics with a relatively light 0++ isosinglet scalar.
The dynamic structure of individual nucleosomes was examined by stretching nucleosomal arrays with a feedback-enhanced optical trap. Forced disassembly of each nucleosome occurred in three stages. ...Analysis of the data using a simple worm-like chain model yields 76 bp of DNA released from the histone core at low stretching force. Subsequently, 80 bp are released at higher forces in two stages: full extension of DNA with histones bound, followed by detachment of histones. When arrays were relaxed before the dissociated state was reached, nucleosomes were able to reassemble and to repeat the disassembly process. The kinetic parameters for nucleosome disassembly also have been determined.
We present a method for defining a lattice realization of the ϕ4 quantum field theory on a simplicial complex in order to enable numerical computation on a general Riemann manifold. The procedure ...begins with adopting methods from traditional Regge calculus (RC) and finite element methods (FEM) plus the addition of ultraviolet counterterms required to reach the renormalized field theory in the continuum limit. The construction is tested numerically for the two-dimensional ϕ4 scalar field theory on the Riemann two-sphere, S2, in comparison with the exact solutions to the two-dimensional Ising conformal field theory (CFT). Numerical results for the Binder cumulants (up to 12th order) and the two- and four-point correlation functions are in agreement with the exact c=1/2 CFT solutions.
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