Density of states techniques for lattice field theories using the functional fit approach (FFA)

Gattringer, Christof; Giuliani, Mario; Lehmann, Alexander; Törek, Pascal

doi:10.48550/arxiv.1511.07176

Cited by 6 publications

(17 citation statements)

References 10 publications

(21 reference statements)

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“…This theory has a real dual formulation, 34,35,41 and can be efficiently simulated with the flux algorithm. 20 It is therefore ideally suited for testing the LLR approach (for a simulation with the related density of states FFA (functional fit approach) see 92,99,100 ). We introduce…”

Section: The Z 3 Theory At Finite Densitiesmentioning

confidence: 99%

Approaches to the sign problem in lattice field theory

Gattringer

Langfeld

2016

Int. J. Mod. Phys. A

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Quantum field theories (QFTs) at finite densities of matter generically involve complex actions. Standard Monte-Carlo simulations based upon importance sampling, which have been producing quantitative first principle results in particle physics for almost fourty years, cannot be applied in this case. Various strategies to overcome this so-called sign problem or complex action problem were proposed during the last thirty years. We here review the sign problem in lattice field theories, focussing on two more recent methods: Dualization to world-line type of representations and the density-of-states approach.

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Section: The Z 3 Theory At Finite Densitiesmentioning

confidence: 99%

Approaches to the sign problem in lattice field theory

Gattringer

Langfeld

2016

Int. J. Mod. Phys. A

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138

145

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“…Here we present an exploratory study of a variant of DoS techniques, the Density of States Functional Fit Approach (DoS FFA) [14,15,16]. Similar to the LLR approach we parameterize the density on small intervals and evaluate restricted vacuum expectation values.…”

Section: Introductionmentioning

confidence: 99%

“…With a one-parameter fit of the Monte Carlo data one then can precisely determine ρ(x) on the corresponding interval. The Dos FFA has been introduced and tested for the Z 3 spin system and was found to reproduce the results of a reference simulation with dual variables for a relatively wide range of parameters [14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Developing and testing the density of states FFA method in the SU(3) spin model

2016

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The Density of States Functional Fit Approach (DoS FFA) is a recently proposed modern density of states technique suitable for calculations in lattice field theories with a complex action problem. In this article we present an exploratory implementation of DoS FFA for the SU(3) spin system at finite chemical potential µ -an effective theory for the Polyakov loop. This model has a complex action problem similar to the one of QCD but also allows for a dual simulation in terms of worldlines where the complex action problem is solved. Thus we can compare the DoS FFA results to the reference data from the dual simulation and assess the performance of the new approach. We find that the method reproduces the observables from the dual simulation for a large range of µ values, including also phase transitions, illustrating that DoS FFA is an interesting approach for exploring phase diagrams of lattice field theories with a complex action problem.arXiv:1607.07340v2 [hep-lat]

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“…In principle, density of states techniques -initially introduced in lattice field theory in [1,2] -are a possible approach and, based on various recent technological developments, were applied in a wide range of applications with complex action problems [3] - [23]. However, the case of treating the complex action problem emerging from a topological term is somewhat subtle, because in the usual formulation with periodic boundary conditions the topological charge becomes quantized to integers in the continuum limit such that the density will approach a superposition of Dirac deltas (see, e.g., [18]). If a geometrical or a fermionic definition is used the topological charge is quantized also at finite lattice constant, resulting in a superposition of Dirac deltas also at finite lattice spacing.…”

Section: Introductory Commentsmentioning

confidence: 99%

Density of states approach for lattice field theory with topological terms

Gattringer¹,

Orasch²

2021

Preprint

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We discuss a new density of states (DoS) approach to solve the complex action problem that is caused by topological terms. The key ingredient is to use open boundary conditions for (at least) one of the directions, such that the quantization of the topological charge is lifted and the density becomes a regular function. We employ the DoS FFA method and compute the density of states as a function of the topological charge. Subsequent integration with suitable factors gives rise to the observables we are interested in. We here explore two test cases: U(1) lattice gauge theory in two dimensions, and SU(2) lattice gauge theory in four dimensions. Since the 2-d case has an exact solution we may use it to assess the method, in particular to establish the equivalence of the open boundary results with the usual choice of periodic boundary conditions. The SU(2) case is a first step of developing the techniques towards their eventual application in full QCD.

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Density of states techniques for lattice field theories using the functional fit approach (FFA)

Cited by 6 publications

References 10 publications

Approaches to the sign problem in lattice field theory

Approaches to the sign problem in lattice field theory

Developing and testing the density of states FFA method in the SU(3) spin model

Density of states approach for lattice field theory with topological terms

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