The Z3 model with the density of states method

Mercado, Ydalia Delgado; Toerek, Pascal; Gattringer, Christof

doi:10.22323/1.214.0203

Cited by 3 publications

(2 citation statements)

References 3 publications

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“…This model has been simulated using complex Langevin techniques and the worm algorithm, the latter providing reference benchmarks for novel approaches. It has been shown [19] that an observable that is particularly sensitive to the sign problem is the phase twist p(µ), defined as 15) where N z and N z are respectively the number of spins pointing along z and z * , the two non-trivial elements of Z(3). In Fig.…”

Section: The Llr Algorithmmentioning

confidence: 99%

The density of state approach to the sign problem

Lucini¹,

Francesconi²,

Holzmann³

et al. 2019

Proceedings of XIII Quark Confinement and the Hadron Spectrum — PoS(Confinement2018)

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Approaches to the sign problem based on the density of states have been recently revived by the introduction of the LLR algorithm, which allows us to compute the density of states itself with exponential error reduction. In this work, after a review of the generalities of the method, we show recent results for the Bose gas in four dimensions, focussing on the identification of possible systematic errors and on methods of controlling the bias they can introduce in the calculation.

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Section: The Llr Algorithmmentioning

confidence: 99%

The density of state approach to the sign problem

Lucini¹,

Francesconi²,

Holzmann³

et al. 2019

Proceedings of XIII Quark Confinement and the Hadron Spectrum — PoS(Confinement2018)

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“…The density of states will be determined using the Linear Logarithmic Relaxation (LLR) algorithm [10,14], which has been shown to provide exponential error reduction in a range of Lattice Gauge Theories applications involving e.g., tunnelling suppression at a first order phase transition [14], the determination of the free energy for a system with shifted boundary conditions [15] and the de-correlation of the topological charge near the continuum limit [16]. Earlier studies of complex action systems with the LLR and the closely related FFA method can be found respectively in [8,[17][18][19][20][21] and [9,[22][23][24] (see also [25]). In this work, we will focus on the full -phase quenched overlap free energy.…”

Section: Introductionmentioning

confidence: 99%

Free energy of the self-interacting relativistic lattice Bose gas at finite density

et al. 2020

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The density of state approach has recently been proposed as a potential route to circumvent the sign problem in systems at finite density. In this study, using the Linear Logarithmic Relaxation (LLR) algorithm, we extract the generalised density of states, which is defined in terms of the imaginary part of the action, for the self-interacting relativistic lattice Bose gas at finite density. After discussing the implementation and testing the reliability of our approach, we focus on the determination of the free energy difference between the full system and its phase-quenched counterpart. Using a set of lattices ranging from 4 4 to 16 4 , we show that in the low density phase, this overlap free energy can be reliably extrapolated to the thermodynamic limit. The numerical precision we obtain with the LLR method allows us to determine with sufficient accuracy the expectation value of the phase factor, which is used in the calculation of the overlap free energy, down to values of O(10 −480 ). When phase factor measurements are extended to the dense phase, a change of behaviour of the overlap free energy is clearly visible as the chemical potential crosses a critical value. Using fits inspired by the approximate validity of mean-field theory, which is confirmed by our simulations, we extract the critical chemical potential as the non-analyticity point in the overlap free energy, obtaining a value that is in agreement with other determinations. Implications of our findings and potential improvements of our methodology are also discussed.

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Density of states approach for lattice field theory with topological terms

Gattringer¹,

Orasch²

2022

Proceedings of the 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021)

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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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The Z3 model with the density of states method

Cited by 3 publications

References 3 publications

The density of state approach to the sign problem

The density of state approach to the sign problem

Free energy of the self-interacting relativistic lattice Bose gas at finite density

Density of states approach for lattice field theory with topological terms

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