Schwinger model with the overlap-Dirac operator: Exact results versus a physics motivated approximation

Giusti, Leonardo; Hoelbling, Christian; Rebbi, C.

doi:10.1103/physrevd.64.054501

Cited by 19 publications

(4 citation statements)

References 41 publications

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“…A particularly interesting study case is that of the Schwinger model [25,26], or QED in one spatial dimension, the simplest gauge theory, which nevertheless exhibits features in common with more complex models (QCD) such as confinement or a non-trivial vacuum, and has been adopted as a benchmark model where to explore lattice gauge theory techniques (see e.g. [27][28][29][30][31] and references cited therein).…”

Section: Introductionmentioning

confidence: 99%

The mass spectrum of the Schwinger model with matrix product states

Bañuls

Cichy

Cirac

et al. 2013

J. High Energ. Phys.

202

267

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Abstract:We show the feasibility of tensor network solutions for lattice gauge theories in Hamiltonian formulation by applying matrix product states algorithms to the Schwinger model with zero and non-vanishing fermion mass. We introduce new techniques to compute excitations in a system with open boundary conditions, and to identify the states corresponding to low momentum and different quantum numbers in the continuum. For the ground state and both the vector and scalar mass gaps in the massive case, the MPS technique attains precisions comparable to the best results available from other techniques.

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Section: Introductionmentioning

confidence: 99%

The mass spectrum of the Schwinger model with matrix product states

Bañuls

Cichy

Cirac

et al. 2013

J. High Energ. Phys.

202

267

View full text Add to dashboard Cite

show abstract

“…[100,101]. Note that while these gauge fields originate from a quenched ensemble, there is no problem in the Schwinger model to reweight them to an arbitrary mass unquenched ensemble [100][101][102][103].…”

Section: B U(1) Gauge Field Casementioning

confidence: 99%

Spectral properties and chiral symmetry violations of (staggered) domain wall fermions in the Schwinger model

Hoelbling

Zielinski

2016

Phys. Rev. D

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We follow up on a suggestion by Adams and construct explicit domain wall fermion operators with staggered kernels. We compare different domain wall formulations, namely the standard construction as well as Boriçi's modified and Chiu's optimal construction, utilizing both Wilson and staggered kernels. In the process, we generalize the staggered kernels to arbitrary even dimensions and introduce both truncated and optimal staggered domain wall fermions. Some numerical investigations are carried out in the (1 + 1)-dimensional setting of the Schwinger model, where we explore spectral properties of the bulk, effective and overlap Dirac operators in the free-field case, on quenched thermalized gauge configurations and on smooth topological configurations. We compare different formulations using the effective mass, deviations from normality and violations of the Ginsparg-Wilson relation as measures of chirality.

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“…An HMC algorithm using a polynomial approximation to the sign function was tested in [33], and found to be inferior to the ZPFE. 3 Earlier work done concerning dynamical overlap fermions in the Schwinger model can be found in [39,40,41,42]. More recently, some exploratory studies in full QCD [26,43,44] have been presented.…”

Section: Introductionmentioning

confidence: 99%

Numerical methods for the QCD overlap operator IV: Hybrid Monte Carlo

Cundy

Krieg

Arnold

et al. 2009

Computer Physics Communications

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The computational costs of calculating the matrix sign function of the overlap operator together with fundamental numerical problems related to the discontinuity of the sign function in the kernel eigenvalues are the major obstacles towards simulations with dynamical overlap fermions using the Hybrid Monte Carlo algorithm. In a previous paper of the present series we introduced optimal numerical approximation of the sign function and have developed highly advanced preconditioning and relaxation techniques which speed up the the inversion of the overlap operator by nearly an order of magnitude.In this fourth paper of the series we construct an HMC algorithm for overlap fermions. We approximate the matrix sign function using the Zolotarev rational approximation, treating the smallest eigenvalues of the Wilson operator exactly within the fermionic force. Based on this we derive the fermionic force for the overlap operator. We explicitly solve the problem of the Dirac delta-function terms arising through zero crossings of eigenvalues of the Wilson operator. The main advantage of this scheme is that its energy violations scale better than O(∆τ 2 ) and thus are comparable with the violations of the standard leapfrog algorithm over the course of a trajectory. We explicitly prove that our algorithm satisfies reversibility and area conservation. We present test results from our algorithm on 4 4 , 6 4 , and 8 4 lattices.

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Schwinger model with the overlap-Dirac operator: Exact results versus a physics motivated approximation

Cited by 19 publications

References 41 publications

The mass spectrum of the Schwinger model with matrix product states

The mass spectrum of the Schwinger model with matrix product states

Spectral properties and chiral symmetry violations of (staggered) domain wall fermions in the Schwinger model

Numerical methods for the QCD overlap operator IV: Hybrid Monte Carlo

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