Sign problem and Monte Carlo calculations beyond Lefschetz thimbles

Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo F.; Ridgway, Gregory W.; Warrington, Neill C.

doi:10.48550/arxiv.1512.08764

Cited by 30 publications

(61 citation statements)

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“…In [11][12][13][14][15] such a deformation x → z t (x) (t ≥ 0) is made according to the antiholomorphic gradient flow:…”

Section: Tempered Lefschetz Thimble Methodsmentioning

confidence: 99%

“…This multimodality of distribution makes the Monte Carlo calculation impractical, especially when contributions from more than one thimble are relevant to estimating expectation values. A key proposal in [12] is to use a finite value of flow time that is large enough to avoid the sign problem but simultaneously is not too large so that the exploration in the configuration space is still possible. However, it is a difficult task to find such value of flow time in a systematic way, as we will mention at the end of this letter.…”

Section: Tempered Lefschetz Thimble Methodsmentioning

confidence: 99%

“…There have been two major approaches to solving the sign problem. One is the complex Langevin method [5], and the other is a class of algorithms utilizing the Lefschetz thimbles [6][7][8][9][10][11][12][13][14][15]. Each has its own advantage and disadvantage.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Applying the tempered Lefschetz thimble method to the Hubbard model away from half filling

Fukuma

Matsumoto

Umeda³

2019

Phys. Rev. D

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The tempered Lefschetz thimble method [14] is a parallel-tempering algorithm to solve the sign problem in Monte Carlo simulations. It uses the flow time of the antiholomorphic gradient flow as a tempering parameter and is expected to tame both the sign and multimodal problems simultaneously. In this letter, we further develop the algorithm so that the expectation values can be estimated precisely with a criterion ensuring global equilibrium and the sufficiency of the sample size. The key is the use of the fact that the expectation values should be the same for all replicas due to Cauchy's theorem. To demonstrate that this algorithm works well, we apply it to the quantum Monte Carlo simulation of the Hubbard model away from half-filling on a two-dimensional lattice of small size, and show that the numerical results agree nicely with exact values.

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“…In [11][12][13][14][15] such a deformation x → z t (x) (t ≥ 0) is made according to the antiholomorphic gradient flow:…”

Section: Tempered Lefschetz Thimble Methodsmentioning

confidence: 99%

Section: Tempered Lefschetz Thimble Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Applying the tempered Lefschetz thimble method to the Hubbard model away from half filling

Fukuma

Matsumoto

Umeda³

2019

Phys. Rev. D

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show abstract

“…Additionally, significant analytical work is needed to identify all the thimbles contributing to the integral. In an earlier paper [7] we proposed a method that sidesteps this task. The idea is to use a class of manifolds generated by the holomorphic gradient flow and parametrized by the flow time T flow interpolating smoothly between the original integration domain (T flow = 0) and the thimble decomposition (T flow = +∞).…”

Section: Introductionmentioning

confidence: 99%

Tempered transitions between thimbles

et al. 2017

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Quantum field theories with complex actions cannot be investigated using importance sampling due to the sign problem. One possible solution is to use the holomorphic gradient flow, a method we introduced related to the Lefschetz thimbles idea. In many cases the probability distribution generated by this method is multi-modal and standard Monte-Carlo sampling fails. We propose an algorithm that incorporates tempered proposals to solve this problem. We apply this algorithm to the 0 + 1 dimensional Thirring model at finite density for a parameter set where standard sampling fails and show that tempered proposals cure this problem.

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“…In this paper, we propose a novel method to create a tensor network for two-dimensional 1 Recently, significant progress has been made also in the Monte Carlo (MC) approach to the sign problem [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], giving rise to a hope that MC simulations can be performed at a reasonable computational cost. Two approaches (TN and MC) may play complementary roles in the future.…”

Section: Introductionmentioning

confidence: 99%

Tensor network approach to 2D Yang-Mills theories

Fukuma

Kadoh

Matsumoto

2021

Preprint

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We propose a novel tensor network representation for two-dimensional Yang-Mills theories with arbitrary compact gauge groups. In this method, tensor indices are directly given by group elements with no direct use of the character expansion. We apply the tensor renormalization group method to this tensor network for SU (2) and SU (3), and find that the free energy density and the energy density are accurately evaluated. We also show that the singular value decomposition of a tensor has a group theoretic structure and can be associated with the character expansion.

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Sign problem and Monte Carlo calculations beyond Lefschetz thimbles

Cited by 30 publications

References 0 publications

Applying the tempered Lefschetz thimble method to the Hubbard model away from half filling

Applying the tempered Lefschetz thimble method to the Hubbard model away from half filling

Tempered transitions between thimbles

Tensor network approach to 2D Yang-Mills theories

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