Surface worm algorithm for abelian Gauge–Higgs systems on the lattice

Mercado, Ydalia Delgado; Gattringer, Christof; Schmidt, A.

doi:10.1016/j.cpc.2013.02.001

Cited by 50 publications

(99 citation statements)

References 39 publications

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“…5) plotted against L on a double logarithmic scale, we do not observe a systematic variation with the spatial extent L and the results from determinations based on τ int,cut , τ int,f it and τ exp,f it agree within a a relative error of 5%. Quoting again the results from the largest volume pair we find z int,cut = 1.3448 (7) and z int,f it = 1.34076 (8), which combine to a value of z int = 1.342 (2). The result for the dynamical critical exponent determined from the exponential autocorrelation time is z exp = 1.3478 (3), and also for q = 4 we find very good agreement of the results for z.…”

Section: Exploratory Assessment Of the Algorithm For Q ≤ 4 (2 Nd Ordesupporting

confidence: 73%

Exploring the worldline formulation of the Potts model

Gattringer¹,

Göschl²,

Törek³

2020

Nuclear Physics B

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We revisit the issue of worldline formulations for the q-state Potts model and discuss a worldline representation in arbitrary dimensions which also allows for magnetic terms. For vanishing magnetic field we implement a Hodge decomposition for resolving the constraints with dual variables, which in two dimensions implies self-duality as a simple corollary. We present exploratory 2-d Monte Carlo simulations in terms of the worldlines, based on worm algorithms. We study both, vanishing and non-zero magnetic field, and explore q between q = 2 and q = 30, i.e., Potts models with continuous, as well as strong first order transitions.

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Section: Exploratory Assessment Of the Algorithm For Q ≤ 4 (2 Nd Ordesupporting

confidence: 73%

Exploring the worldline formulation of the Potts model

Gattringer¹,

Göschl²,

Törek³

2020

Nuclear Physics B

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“…For the Yang-Mills part, it is advantageous to perform a character expansion 5) where the factor c 0 (β) can be neglected as it is independent of gauge links and cancels in expectation values. In earlier publications [8,9,23], we have shown how to compute the effective gauge theory up to rather high orders in the fundamental character expansion coefficient u(β) ≡ a f (β) = β 18 + .…”

Section: Pure Gauge Theorymentioning

confidence: 99%

“…Note that the Pauli principle for N f = 1 does not admit spin 1/2 doublets. The quark number density and the energy density then follow as 5) where the derivative with respect to a has to be taken at constant fugacity exp(aµN τ ) and we have made use of eq. (2.50).…”

Section: Jhep09(2014)131mentioning

confidence: 99%

“…In order to reach higher chemical potentials and/or low temperatures, methods are required which at least potentially may solve this problem. Among these are Complex Langevin Dynamics (CLD) [2,3], transformation of the degrees of freedom into so-called dual variables as demonstrated in scalar models [4,5], and the formulation of quantum field theories on a Lefshetz thimble [6]. In particular, CLD has recently been applied to full QCD in a previously inaccessible parameter range [7].…”

Section: Introductionmentioning

confidence: 99%

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Heavy dense QCD and nuclear matter from an effective lattice theory

Langelage

Neuman

Philipsen

2014

J. High Energ. Phys.

140

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A three-dimensional effective lattice theory of Polyakov loops is derived from QCD by expansions in the fundamental character of the gauge action, u, and the hopping parameter, κ, whose action is correct to κ n u m with n + m = 4. At finite baryon density, the effective theory has a sign problem which meets all criteria to be simulated by complex Langevin as well as by Monte Carlo on small volumes. The theory is valid for the thermodynamics of heavy quarks, where its predictions agree with simulations of full QCD at zero and imaginary chemical potential. In its region of convergence, it is moreover amenable to perturbative calculations in the small effective couplings. In this work we study the challenging cold and dense regime. We find unambiguous evidence for the nuclear liquid gas transition once the baryon chemical potential approaches the baryon mass, and calculate the nuclear equation of state in the limit of heavy baryons. In particular, we find a negative binding energy per nucleon causing the condensation, whose absolute value decreases exponentially as mesons get heavier. For decreasing meson mass, we observe a first order liquid gas transition with an endpoint at some finite temperature, as well as a gap between the onset of isospin and baryon condensation.

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“…An important feature is that the original symmetries of the system are translated into constraints such as flux conservation or restrictions on the allowed occupation numbers. Typically these constraints are central in Monte Carlo simulations such as in the Worm algorithm [13] or generalizations thereof [14]. Dual representations are in general not unique: a model can have several dual representations which may have different residual sign problems.…”

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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Surface worm algorithm for abelian Gauge–Higgs systems on the lattice

Cited by 50 publications

References 39 publications

Exploring the worldline formulation of the Potts model

Exploring the worldline formulation of the Potts model

Heavy dense QCD and nuclear matter from an effective lattice theory

New dual representation for staggered lattice QCD

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