Background field method in the gradient flow

Suzuki, Hiroshi

doi:10.22323/1.251.0304

Cited by 2 publications

(3 citation statements)

References 22 publications

(50 reference statements)

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“…This was observed in Refs. [15] and [12]. We have confirmed it and found that it produces positive/negative cancellation in the confinement phase.…”

Section: Resultssupporting

confidence: 80%

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Sign problem in finite density lattice QCD

Goy

Bornyakov

Boyda

et al. 2017

Progress of Theoretical and Experimental Physics

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The canonical approach, which was developed for solving the sign problem, may suffer from a new type of sign problem. In the canonical approach, the grand partition function is written as a fugacity expansion: Z G (µ, T ) = n Z C (n, T )ξ n , where ξ = exp(µ/T ) is the fugacity, and Z C (n, T ) are given as averages over a Monte Carlo update, z n . We show that the complex phase of z n is proportional to n at each Monte Carlo step. Although z n take real positive values, the values of z n fluctuate rapidly when n is large, especially in the confinement phase, which gives a limit on n. We discuss possible remedies for this problem.

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“…This was observed in Refs. [15] and [12]. We have confirmed it and found that it produces positive/negative cancellation in the confinement phase.…”

Section: Resultssupporting

confidence: 80%

“…The arguments from Eqs. ( 10) to (15) tell us that the phase of the winding number W n determines the phase of z n . Although each W n contributes z l , the largest effect comes from W ±1 .…”

Section: Discussionmentioning

confidence: 99%

Sign problem in finite density lattice QCD

Goy

Bornyakov

Boyda

et al. 2017

Progress of Theoretical and Experimental Physics

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“…Physical outcomes, its comparison with the multi-parameter reweighting method, the moments of the baryon number and an analysis of the high precision calculation are discussed by Ref. [5], [6], [7] and [8], respectively.…”

Section: Chiral Chemical Potentialmentioning

confidence: 99%

Beating the sign problem in finite density lattice QCD

Nakamura¹,

Fukuda

Oka

et al. 2016

Proceedings of the 33rd International Symposium on Lattice Field Theory — PoS(LATTICE 2015)

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We report our recent project to study the QCD phase diagram by the canonical approach (CA), which is expected to solve the sign problem. First we briefly describe the sign problem and several approaches to fight against it. Then we argue that the CA may be a break-through if we combine it with the multiple precision calculation. We study the method using the hopping parameter expansion (HPE), in order to investigate how the CA works. We show explicitly how we calculate the winding number in HPE and obtain the fugacity expansion whose coefficients are the canonical partition functions. Finally we discuss dark sides of the current CA, which should be beaten for the method to become a real tool of QCD phase explorers.

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Background field method in the gradient flow

Cited by 2 publications

References 22 publications

Sign problem in finite density lattice QCD

Sign problem in finite density lattice QCD

Beating the sign problem in finite density lattice QCD

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