Monte Carlo calculations of the finite density Thirring model

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

doi:10.1103/physrevd.95.014502

Cited by 73 publications

(91 citation statements)

References 27 publications

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“…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%

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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Section: Introductionmentioning

confidence: 99%

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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“…However, when there exists more than one thimbles, the transition from one to another does not occur during the Monte Carlo simulation and hence the ergodicity is violated in this limit. Therefore, there is an optimal flow time in general [23][24][25]. (See refs.…”

Section: Jhep06(2017)023mentioning

confidence: 99%

Combining the complex Langevin method and the generalized Lefschetz-thimble method

Nishimura

Shimasaki

2017

J. High Energ. Phys.

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Abstract:The complex Langevin method and the generalized Lefschetz-thimble method are two closely related approaches to the sign problem, which are both based on complexification of the original dynamical variables. The former can be viewed as a generalization of the stochastic quantization using the Langevin equation, whereas the latter is a deformation of the integration contour using the so-called holomorphic gradient flow. In order to clarify their relationship, we propose a formulation which combines the two methods by applying the former method to the real variables that parametrize the deformed integration contour in the latter method. Three versions, which differ in the treatment of the residual sign problem in the latter method, are considered. By applying them to a single-variable model, we find, in particular, that one of the versions interpolates the complex Langevin method and the original Lefschetz-thimble method.

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“…(3.1) that includes a way of bypassing the computation of the jacobian by adapting the Grady algorithm [24,25] originally created to deal with fermion determinants. The main idea [26] is to make a modified proposal that is isotropic in the variable φ T (ζ), not in ζ, and then correct for that by modifying the accept/reject step. The proposal probability is given by…”

Section: Epj Web Of Conferencesmentioning

confidence: 99%

“…Consider, for instance, a 1 + 1 dimensional φ 4 theory [26]. The first problem is that the tangent plane to the critical point φ c = 0 is not real and, in some directions in field space, points towards the imaginary direction.…”

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confidence: 99%