Flow-based sampling in the lattice Schwinger model at criticality

Albergo, Michael S.; Boyda, Denis; Cranmer, K.; Hackett, Daniel C.; Kanwar, Gurtej; Racanière, Sébastien; Rezende, Danilo Jimenez; Romero-López, Fernando; Shanahan, Phiala E.; Urban, Julian M.

doi:10.1103/physrevd.106.014514

Cited by 25 publications

(10 citation statements)

References 43 publications

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“…For example, in the multi-flavor Schwinger model there is a mass shift analogous to (3) which may again improve the rate of convergence to the continuum limit. In particular, the two-flavor model [30] should be quite accessible numerically (for recent results using Euclidean lattice theory, see [38]. We also plan to use the Hamiltonian lattice theory to study SU (N ) gauge theory coupled an adjoint Majorana fermion.…”

Section: Discussionmentioning

confidence: 99%

Discrete Chiral Symmetry and Mass Shift in Lattice Hamiltonian Approach to Schwinger Model

Dempsey¹,

Klebanov²,

Pufu³

et al. 2022

Preprint

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We revisit the lattice formulation of the Schwinger model using the Kogut-Susskind Hamiltonian approach with staggered fermions. This model, introduced by Banks et al., contains the mass term m lat n (−1) n χ † n χn, and setting it to zero is often assumed to provide the lattice regularization of the massless Schwinger model. We instead argue that the relation between the lattice and continuum mass parameters should be taken as m lat = m − 1 8 e 2 a. The model with m = 0 is shown to possess a discrete chiral symmetry that is generated by the unit lattice translation accompanied by the shift of the θ-angle by π. While the mass shift vanishes as the lattice spacing a approaches zero, we find that including this shift greatly improves the rate of convergence to the continuum limit. We demonstrate the faster convergence using both numerical diagonalizations of finite lattice systems, as well as extrapolations of the lattice strong coupling expansions.

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Section: Discussionmentioning

confidence: 99%

Discrete Chiral Symmetry and Mass Shift in Lattice Hamiltonian Approach to Schwinger Model

Dempsey¹,

Klebanov²,

Pufu³

et al. 2022

Preprint

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“…It is noteworthy that the methods described so far are already sufficient to apply normalizing flows to theories with fermions and theories in arbitrary spacetime dimensions, including the particularly challenging task of lattice QCD, as demonstrated by exploratory studies performed in Refs. [54][55][56][57][58][59]. These studies have shown that there are no theoretical obstacles to flow-based sampling for almost all lattice field theories of interest.…”

Section: Fermions and Application To Qcdmentioning

confidence: 99%

“…In principle, flow-based models can be optimized to reproduce this target distribution just as for an ordinary bosonic theory. Early studies demonstrated that it was possible to train models to closely reproduce this effective action using exact evaluations of the determinant [55,56]. However, just as for Hybrid Monte Carlo (HMC), this approach does not scale favorably with the number of lattice sites.…”

Section: Dynamical Fermionsmentioning

confidence: 99%

Flow-based sampling for fermionic lattice field theories

et al. 2021

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Critical slowing down and topological freezing severely hinder Monte Carlo sampling of lattice field theories as the continuum limit is approached. Recently, significant progress has been made in applying a class of generative machine learning models, known as "flow-based" samplers, to combat these issues. These generative samplers also enable promising practical improvements in Monte Carlo sampling, such as fully parallelized configuration generation. These proceedings review the progress towards this goal and future prospects of the method.

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“…Bespoke flow architectures tailored to this application have been constructed, including gauge-equivariant architectures designed for Abelian and non-Abelian gauge field theories [30,31], and methods to incorporate fermions [32,46]. Proof-of-principle implementations have demonstrated success in ameliorating important challenges such as critical slowing-down and topological freezing, as well as the computation of thermodynamic quantities, in theories ranging from scalar field theory [5,28,35,39,76] through Yukawa theory [32], to the Schwinger model [9,43] and SU(3) gauge field theory with fermions in two dimensions [46].…”

Section: Introductionmentioning

confidence: 99%

Sampling QCD field configurations with gauge-equivariant flow models

Abbott¹,

Albergo²,

Botev³

et al. 2022

Preprint

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Machine learning methods based on normalizing flows have been shown to address important challenges, such as critical slowing-down and topological freezing, in the sampling of gauge field configurations in simple lattice field theories. A critical question is whether this success will translate to studies of QCD. This Proceedings presents a status update on advances in this area. In particular, it is illustrated how recently developed algorithmic components may be combined to construct flow-based sampling algorithms for QCD in four dimensions. The prospects and challenges for future use of this approach in at-scale applications are summarized.

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Flow-based sampling in the lattice Schwinger model at criticality

Cited by 25 publications

References 43 publications

Discrete Chiral Symmetry and Mass Shift in Lattice Hamiltonian Approach to Schwinger Model

Discrete Chiral Symmetry and Mass Shift in Lattice Hamiltonian Approach to Schwinger Model

Flow-based sampling for fermionic lattice field theories

Sampling QCD field configurations with gauge-equivariant flow models

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