A thick-restart Lanczos type method for Hermitian J-symmetric eigenvalue problems

Ishikawa, Ken-ichi; Sogabe, Tomohiro

doi:10.1007/s13160-020-00435-x

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…With the parameters, the value of the total Hamiltonian is precisely evaluated for the Metropolis test. To compute the exterior eigenvalues of 𝑄 2 𝑊 , which has the symmetry 𝐵(𝑄 2 𝑊 )𝐵 −1 = (𝑄 2 𝑊 ) 𝑇 with 𝐵 = 𝛾 5 𝐶 resulting in a two-folded eigenspectrum, we employ an improved thick-restart Lanczos type algorithm [9] to treat the degeneracy.…”

Section: Simulation Methodsmentioning

confidence: 99%

Large $N$ simulation of the twisted reduced matrix model with an adjoint Majorana fermion

Butti¹,

Pérez²,

González-Arroyo³

et al. 2021

Preprint

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To investigate the properties of the large 𝑁 limit of N = 1 SUSY Yang-Mills theory, we have started a study for a reduced matrix model with an adjoint Majorana fermion. The gauge action is based on the Wilson action and the adjoint-fermion one is the Wilson-Dirac action on a reduced lattice with twisted gauge boundary condition. We employ the RHMC algorithm in which the absolute value of the Pfaffian is incorporated. The sign of the Pfaffian is included with the re-weighting method and separately measured as an observable. In this talk, we show the configuration generation status towards the large 𝑁 limit and the behavior of the lowest/lower eigenvalue(s) of the Wilson-Dirac adjoint fermion operator. We investigated the sign of the Pfaffian and the critical hopping parameters for the chiral limit. The sign of the Pfaffian is always positive on the configurations we have generated. The critical hopping parameters derived from the eigenvalues of the Dirac operator are consistent with those derived from the PCAC mass relation with non-singlet flavor adjoint fermions.

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Section: Simulation Methodsmentioning

confidence: 99%

Large $N$ simulation of the twisted reduced matrix model with an adjoint Majorana fermion

Butti¹,

Pérez²,

González-Arroyo³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…with J = Cγ 5 [44]. For the coefficient set used during the MD evolution, which should be invariant during the period of generation of configurations, we fix a lower accuracy ∆ R < 10 −5 -10 −8 and select a parameter set for (N R , a, b), with a and b tuned to cover the eigenvalue range determined during the thermalization period.…”

Section: Jhep07(2022)074mentioning

confidence: 99%

Scale setting for large-N SUSY Yang-Mills on the lattice

Butti

Pérez

González-Arroyo

et al. 2022

J. High Energ. Phys.

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In this paper we study the large N limit of four-dimensional Supersymmetric Yang-Mills on the lattice using twisted reduced models. We have generated configurations with dynamical massive gluinos and various lattice ’t Hooft couplings, and verified that the Pfaffian remains positive. We have determined the lattice spacing in terms of various observables obtaining compatible results. Extrapolating to the massless gluino limit we obtain the lattice spacing dependence on the bare couplings for the supersymmetric theory. The observed dependence goes along the expected behaviour predicted by perturbation theory.

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“…With the parameters, the value of the total Hamiltonian is precisely evaluated for the Metropolis test. To compute the exterior eigenvalues of 2 , which has the symmetry ( 2 ) −1 = ( 2 ) with = 5 resulting in a two-folded eigenspectrum, we employ an improved thick-restart Lanczos type algorithm [9] to treat the degeneracy.…”

Section: Pos(lattice2021)334mentioning

confidence: 99%

Large $N$ simulation of the twisted reduced matrix model with an adjoint Majorana fermion

Butti¹,

Pérez²,

González-Arroyo³

et al. 2022

Proceedings of the 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021)

Self Cite

View full text Add to dashboard Cite

To investigate the properties of the large limit of N = 1 SUSY Yang-Mills theory, we have started a study for a reduced matrix model with an adjoint Majorana fermion. The gauge action is based on the Wilson action and the adjoint-fermion one is the Wilson-Dirac action on a reduced lattice with twisted gauge boundary condition. We employ the RHMC algorithm in which the absolute value of the Pfaffian is incorporated. The sign of the Pfaffian is included with the re-weighting method and separately measured as an observable. In this talk, we show the configuration generation status towards the large limit and the behavior of the lowest/lower eigenvalue(s) of the Wilson-Dirac adjoint fermion operator. We investigated the sign of the Pfaffian and the critical hopping parameters for the chiral limit. The sign of the Pfaffian is always positive on the configurations we have generated. The critical hopping parameters derived from the eigenvalues of the Dirac operator are consistent with those derived from the PCAC mass relation with non-singlet flavor adjoint fermions.

show abstract

A thick-restart Lanczos type method for Hermitian J-symmetric eigenvalue problems

Cited by 4 publications

References 19 publications

Large $N$ simulation of the twisted reduced matrix model with an adjoint Majorana fermion

Large $N$ simulation of the twisted reduced matrix model with an adjoint Majorana fermion

Scale setting for large-N SUSY Yang-Mills on the lattice

Large $N$ simulation of the twisted reduced matrix model with an adjoint Majorana fermion

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