Lefschetz-thimble analysis of the sign problem in one-site fermion model

Tanizaki, Yuya; Hidaka, Yoshimasa; Hayata, Tomoya

doi:10.1088/1367-2630/18/3/033002

Cited by 92 publications

(92 citation statements)

References 71 publications

(133 reference statements)

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“…When we were finishing this and the related articles, we were informed by Y. Hidaka that they have obtained the similar result about the multi-thimble contributions necessary to reproduce the non-analytic behavior of observables in the one-site Hubberd model [63]. We would like to thank him for sharing their result with us.…”

Section: Acknowledgmentsmentioning

confidence: 83%

Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density

Fujii

Kamata

Kikukawa

2015

J. High Energ. Phys.

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Abstract:We consider the one-dimensional massive Thirring model formulated on the lattice with staggered fermions and an auxiliary compact vector (link) field, which is exactly solvable and shows a phase transition with increasing the chemical potential of fermion number: the crossover at a finite temperature and the first order transition at zero temperature. We complexify its path-integration on Lefschetz thimbles and examine its phase transition by hybrid Monte Carlo simulations on the single dominant thimble. We observe a discrepancy between the numerical and exact results in the crossover region for small inverse coupling β and/or large lattice size L, while they are in good agreement in the lower and higher density regions. We also observe that the discrepancy persists in the continuum limit to keep the temperature finite and it becomes more significant toward the low-temperature limit. This numerical result is consistent with our analytical study of the model and implies that the contributions of subdominant thimbles should be summed up in order to reproduce the first order transition in the low-temperature limit.

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Section: Acknowledgmentsmentioning

confidence: 83%

Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density

Fujii

Kamata

Kikukawa

2015

J. High Energ. Phys.

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“…This example also demonstrates that in using Lefschetz thimbles, for example, either in Euclidean semi-classics or real time semi-classics (with sign problems) [110,111] or in lattice simulations [101][102][103][104], all thimbles whose Stokes multipliers are non-zero must be summed over. Numerical evidence for the correctness of this perspective is also given in [105][106][107][108][109].…”

Section: Hidden Topological Angles and Complex Saddlesmentioning

confidence: 86%

New Nonperturbative Methods in Quantum Field Theory: From Large-NOrbifold Equivalence to Bions and Resurgence

Dunne

Ünsal

2016

Annu. Rev. Nucl. Part. Sci.

112

170

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We present a broad conceptual introduction to some new ideas in non-perturbative QFT. The large-N orbifold-orientifold equivalence connects a natural large-N limit of QCD to QCD with adjoint fermions. QCD(adj) with periodic boundary conditions and double-trace deformation of Yang-Mills theory satisfy large-N volume independence, a type of orbifold equivalence. Certain QFTs that satisfy volume independence at N = ∞ exhibit adiabatic continuity at finite-N , and also become semi-classically calculable on small R 3 × S 1 . We discuss the role of monopole-instantons, and magnetic and neutral bion saddles in connection to mass gap, and center and chiral symmetry realizations. Neutral bions also provide a weak coupling semiclassical realization of infrared-renormalons. These considerations help motivate the necessity of complexification of path integrals (Picard-Lefschetz theory) in semi-classical analysis, and highlights the importance of hidden topological angles. Finally, we briefly review the resurgence program, which potentially provides a novel non-perturbative continuum definition of QFT. All these ideas are continuously connected.Keywords: large-N orbifold and orientifold equivalence, volume independence, double-trace deformations, adiabatic continuity, semi-classical calculability, magnetic and neutral bions, Picard-Lefschetz theory of path integration, and resurgence arXiv:1601.03414v1 [hep-th]

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“…In principle, the integral over this manifold does not have a sign problem. Specific algorithms to perform the integration over a thimble were suggested and applied to a variety of simple toy models with bosonic degrees of freedom [2][3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Sign problem and Monte Carlo calculations beyond Lefschetz thimbles

Alexandru

Başar

Bedaque

et al. 2016

J. High Energ. Phys.

164

157

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We point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part of the action ("Lefschetz thimble"). We describe a family of such manifolds that interpolate between the tangent space at one critical point (where the sign problem is milder compared to the real plane but in some cases still severe) and the union of relevant thimbles (where the sign problem is mild but a multimodal distribution function complicates the Monte Carlo sampling). We exemplify this approach using a simple 0+1 dimensional fermion model previously used on sign problem studies and show that it can solve the model for some parameter values where a solution using Lefschetz thimbles was elusive.

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Lefschetz-thimble analysis of the sign problem in one-site fermion model

Cited by 92 publications

References 71 publications

Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density

Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density

New Nonperturbative Methods in Quantum Field Theory: From Large-NOrbifold Equivalence to Bions and Resurgence

Sign problem and Monte Carlo calculations beyond Lefschetz thimbles

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