Temporal Correlators in the Continuous Time Formulation of Strong Coupling Lattice QCD

Klegrewe, Marc; Unger, Wolfgang

doi:10.22323/1.334.0182

Cited by 2 publications

(2 citation statements)

References 9 publications

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“…More recently also the leading order gauge corrections have been included [39,40]. At strong coupling, also the fermion bag approach has been used [41,42] and continuous time methods have been applied [43,44]. Beyond the leading order, a dual formulation for lattice QCD is notoriously difficult.…”

Section: Introductionmentioning

confidence: 99%

New dual representation for staggered lattice QCD

Gagliardi

Unger

2020

Phys. Rev. D

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We propose a new strategy to evaluate the partition function of lattice QCD with Wilson gauge action coupled to staggered fermions, based on a strong coupling expansion in the inverse bare gauge coupling β = 2N/g 2 . Our method makes use of the recently developed formalism to evaluate the SU(N ) 1−link integrals and consists in an exact rewriting of the partition function in terms of a set of additional dual degrees of freedom which we call "Decoupling Operator Indices" (DOI). The method is not limited to any particular number of dimensions or gauge group U(N ), SU(N ). In terms of the DOI the system takes the form of a Tensor Network which can be simulated using Wormlike algorithms. Higher order β-corrections to strong coupling lattice QCD can be, in principle, systematically evaluated, helping to answer the question whether the finite density sign problem remains mild when plaquette contributions are included. Issues related to the complexity of the description and strategies for the stochastic evaluation of the partition function are discussed.

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Section: Introductionmentioning

confidence: 99%

New dual representation for staggered lattice QCD

Gagliardi

Unger

2020

Phys. Rev. D

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“…There are many approaches to the sign problem as discussed in the present lattice meeting: Taylor expansion in µ/T [2,3,4], the imaginary chemical potential with analytical continuation or for the canonical ensemble [5,6], and the strong coupling approach [7,8] are the mature and useful methods to investigate finite density QCD, but it seems that we cannot reach cold dense matter in the continuum limit. Recently, integral methods in the complexified variable space have been attracting attention: the Lefschetz thimble method [9], the Complex Langevin method [10,11,12,13,14,15], and the path optimization method [16,17,18] are categorized to the complexified variable method.…”

Section: Introductionmentioning

confidence: 99%

Path optimization method with use of neural network for the sign problem in field theories

Ohnishi¹,

Mori²,

Kashiwa³

2019

Proceedings of the 36th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2018)

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We investigate the sign problem in field theories by using the path optimization method with use of the neural network. For theories with the sign problem, integral in the complexified variable space is a promising approach to obtain a finite (non-zero) average phase factor. In the path optimization method, the imaginary part of variables are given as functions of the real part, y i = y i ({x}), and are optimized to enhance the average phase factor. The feedforward neural network can be used to give and to optimize functions with many variables. The combined framework, the path optimization with use of the neural network, is applied to the complex φ 4 theory at finite density, the 0+1 dimensional QCD at finite density, and the Polyakov loop extended Nambu-Jona-Lasinio (PNJL) model, all of which have the sign problem. In these cases, the average phase factor is found to be enhanced significantly. In the complex φ 4 theory, it is demonstrated that the number density is calculated at a high precision. On the optimized path, the imaginary part is found to have strong correlation with the real part on the temporal nearest neighbor site. In the 0+1 dimensional QCD, we compare the results in two different treatments of the link variable: optimization after the diagonal gauge fixing and optimization without the diagonal gauge fixing. These two methods show consistent eigenvalue distribution of the link variables. In the PNJL model with homogeneous field ansatz, finite volume results approach the mean field results as expected, and the phase transition behavior can be described.

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Temporal Correlators in the Continuous Time Formulation of Strong Coupling Lattice QCD

Cited by 2 publications

References 9 publications

New dual representation for staggered lattice QCD

New dual representation for staggered lattice QCD

Path optimization method with use of neural network for the sign problem in field theories

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