Solving the sign problems of the massless lattice Schwinger model with a dual formulation

Gattringer, Christof; Kloiber, T.; Sazonov, Vasily

doi:10.1016/j.nuclphysb.2015.06.017

Cited by 53 publications

(80 citation statements)

References 27 publications

(22 reference statements)

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“…This additional constraint makes the system much more stiff in a Monte Carlo simulation and the insertion of additional winding loops, i.e., additional charges is rare. This has, e.g., been observed in the simulation [29][30][31] of the worldline form [32] of the massless Schwinger model. It was found that in the grand canonical worldline simulation in particular the particle number suffers from very long autocorrelation times.…”

Section: Canonical Worldline Simulationssupporting

confidence: 56%

“…A canonical worldline simulation as we have described here overcomes this problem, since the net-winding number of the fermion loops and thus the particle number is kept fixed. First tests with simulations of the worldline form [32] have shown that with the canonical worldline approach autocorrelation problems are much milder.…”

Section: Canonical Worldline Simulationsmentioning

confidence: 99%

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New techniques and results for worldline simulations of lattice field theories

2018

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Abstract. We use the complex φ 4 field at finite density as a model system for developing further techniques based on worldline formulations of lattice field theories. More specifically we: 1) Discuss new variants of the worm algorithm for updating the φ 4 theory and related systems with site weights. 2) Explore the possibility of canonical simulations in the worldline formulation. 3) Study the connection of 2-particle condensation at low temperature to scattering parameters of the theory.

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Section: Canonical Worldline Simulationssupporting

confidence: 56%

Section: Canonical Worldline Simulationsmentioning

confidence: 99%

New techniques and results for worldline simulations of lattice field theories

2018

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“…Before we end this section, we would like to comment on the connection between our proof for the absence of the sign problem here and the one given in Ref. [29] for the massless Schwinger model. As shown in the previous work, the presence of gauge fields allows us to absorb the staggered fermion phase factors into the gauge fields.…”

Section: World Line Representationmentioning

confidence: 69%

Benchmark results in the 2D lattice Thirring model with a chemical potential

2018

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We study the two-dimensional lattice Thirring model in the presence of a fermion chemical potential. Our model is asymptotically free and contains massive fermions that mimic a baryon and light bosons that mimic pions. Hence, it is a useful toy model for QCD, especially since it, too, suffers from a sign problem in the auxiliary field formulation in the presence of a fermion chemical potential. In this work, we formulate the model in both the world line and fermion-bag representations and show that the sign problem can be completely eliminated with open boundary conditions when the fermions are massless. Hence, we are able accurately compute a variety of interesting quantities in the model, and these results could provide benchmarks for other methods that are being developed to solve the sign problem in QCD.

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“…For fermions in a worldline representation obtained from Grassmann integration, the Pauli principle requires that each site of the lattice is occupied exactly once with a fermionic element, i.e., a monomer, a dimer or a fermion loop (see, e.g., [6]). When increasing the chemical potential temporally winding loops start to dominate.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…In this paper we will compare the results from canonical and grand canonical simulations. Before we discuss the canonical approach in the worldline representation, we briefly comment on the numerical simulation of the grand canonical ensemble described by (3) - (6). For a more detailed discussion see [4].…”

Section: The Model and Its Worldline Representationmentioning

confidence: 99%

Canonical simulations with worldlines: An exploratory study in ϕ24 lattice field theory

Orasch

Gattringer

2018

Int. J. Mod. Phys. A

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In this letter we explore the perspectives for canonical simulations in the worldline formulation of a lattice field theory. Using the charged φ 4 field in two dimensions as an example we present the details of the canonical formulation based on worldlines and outline algorithmic strategies for canonical worldline simulations. We discuss the steps for converting the data from the canonical approach to the grand canonical picture which we use for cross-checking our results. The canonical approach presented here can easily be generalized to other lattice field theories with a worldline representation. Introductory remarksImplementing a clean ab-initio calculation of lattice QCD at finite density is one of the great open challenges in the field. The reason for the difficulties is the fact that at non-zero chemical potential µ the action S becomes complex and the Boltzmann factor exp(−S) cannot be used as a weight factor in a Monte Carlo simulation. Among the different approaches for overcoming that so-called complex action problem are canonical simulations where one works at fixed net baryon number, i.e., at a fixed density. The key challenge for implementing the canonical strategy in QCD is the projection to the desired quark or baryon number: in the conventional path integral representation the quark number is not an integer valued observable and the fermion determinant has to be decomposed into temporal winding classes for the gauge loops it consists of. Various strategies for that task can be found in the literature. They either use different expansions of the fermion determinant or Fourier transformation of the determinant with respect to imaginary chemical potential (see [1] for some examples). However, so far the results for canonical lattice QCD are restricted to small volumes and low densities [1].In recent years an alternative formulation based on worldlines was found and explored for several lattice field theories (see [2] for reviews given at the yearly lattice conference series on that topic). In the worldline (or dual) formulation the partition function Z is exactly rewritten in terms of new variables, such that Z becomes a sum over configurations of worldlines. The corresponding weights for the worldline configurations are real and positive also at non-zero chemical potential and the complex action problem is overcome completely in such a worldline representation.

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Solving the sign problems of the massless lattice Schwinger model with a dual formulation

Cited by 53 publications

References 27 publications

New techniques and results for worldline simulations of lattice field theories

New techniques and results for worldline simulations of lattice field theories

Benchmark results in the 2D lattice Thirring model with a chemical potential

Canonical simulations with worldlines: An exploratory study in ϕ24 lattice field theory

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