New techniques and results for worldline simulations of lattice field theories

Giuliani, Mario; Orasch, Oliver; Gattringer, Christof

doi:10.1051/epjconf/201817507007

Cited by 6 publications

(12 citation statements)

References 33 publications

(86 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Analytically integrating over phase fluctuations using a change of variables similar to the dual lattice variables employed in Ref. [43] enables calculations of correlation functions that avoid sign and StN problems in (0 + 1)D complex scalar field theory, but it remains challenging to extend similar analytic integration methods to more complicated theories such as LQCD [7,[44][45][46][47][48][49]. Instead, a new method is explored in this work in which phase differences are "unwrapped," or numerically integrated over a series of spacetime separations.…”

Section: Introductionmentioning

confidence: 99%

Phase unwrapping and one-dimensional sign problems

2018

View full text Add to dashboard Cite

Sign problems in path integrals arise when different field configurations contribute with different signs or phases. Phase unwrapping describes a family of signal processing techniques in which phase differences between elements of a time series are integrated to construct noncompact unwrapped phase differences. By combining phase unwrapping with a cumulant expansion, path integrals with sign problems arising from phase fluctuations can be systematically approximated as linear combinations of path integrals without sign problems. This work explores phase unwrapping in zero-plus-one-dimensional complex scalar field theory. Results with improved signal-to-noise ratios for the spectrum of scalar field theory can be obtained from unwrapped phases, but the size of cumulant expansion truncation errors is found to be undesirably sensitive to the parameters of the phase unwrapping algorithm employed. It is argued that this numerical sensitivity arises from discretization artifacts that become large when phases fluctuate close to singularities of a complex logarithm in the definition of the unwrapped phase.1 Other interesting LQCD observables face distinct StN problems. For instance, isoscalar meson correlation functions are uncharged under U (1) symmetries and possess exponential StN problems but not U (1) phase fluctuations. Excited-state energies are extracted from differences of correlation functions with the same quantum numbers and face StN problems arising from the exponentially precise cancellations needed to project out ground-state contributions and leave exponentially faster decaying excited-state contributions. In large nuclei, StN problems associated with MeV excitation energies are negligible compared to the phase fluctuation StN problem associated with the multi-GeV rest mass of the nucleus. LQCD calculations of isoscalar mesons and exotic hadrons conversely face StN problems primarily from sources besides U (1) phase fluctuations, and phase unwrapping is not immediately applicable to these systems. 2 Cumulant expansions of noncompact "extensive phases" have also been applied to sign problems in QCD and other theories at nonzero chemical potential [51][52][53][54][55][56].

show abstract

Section: Introductionmentioning

confidence: 99%

Phase unwrapping and one-dimensional sign problems

2018

View full text Add to dashboard Cite

show abstract

“…The dual variables, such as worldlines, fermion bags, loops, dimers, plaquette occupation numbers, can have manifestly real and positive weights and MC simulations or other approaches are then possible. The strategy is particularly well-suited in bosonic theories and Abelian gauge theories, such as the φ 4 theory [122], the Abelian gauge-Higgs model [123] or the Schwinger model [124,125]. The fermion bag approach was used, e.g., to solve massless fermionic models such as the two-and three-dimensional Thirring models [126][127][128] or models belonging to the Ising Gross-Neveu universality class [129].…”

Section: B Overcoming the Sign Problem In Lqcdmentioning

confidence: 99%

Review on novel methods for lattice gauge theories

2020

View full text Add to dashboard Cite

Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum chromodynamics. Yet, some very relevant problems remain inherently challenging, such as real time evolution, or the presence of a chemical potential, cases in which Monte Carlo simulations are hindered by a sign problem.In the last few years, a number of possible alternatives have been put forward, based on quantum information ideas, which could potentially open the access to areas of research that have so far eluded more standard methods. They include tensor network calculations, quantum simulations with different physical platforms and quantum computations, and constitute nowadays a vibrant research area. Experts from different fields, including experimental and theoretical high energy physics, condensed matter, and quantum information, are turning their attention to these interdisciplinary possibilities, and driving the progress of the field. The aim of this article is to review the status and perspectives of these new avenues for the exploration of lattice gauge theories.

show abstract

“…The Euclidean action for φ 4 2 lattice field theory in the conventional grand canonical formulation reads…”

Section: The Model and Its Worldline Representationmentioning

confidence: 99%

“…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]. In the worldline form we have two sets of dynamical variables living on the links: k x,ν ∈ Z and a x,ν ∈ N 0 (which can be viewed as generating the weight of the k x,ν configurations).…”

Section: The Model and Its Worldline Representationmentioning

confidence: 99%

“…In [4] it is shown how the site weights at the two endpoints of a link visited by the worm can be distributed such that detailed balance is implemented correctly. Furthermore we used an additional amplitude factor for the starting and terminating steps of the worm to optimize the performance in different regions of parameter space (for details see [4]). …”

Section: The Model and Its Worldline Representationmentioning

confidence: 99%

See 1 more Smart Citation

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

Orasch

Gattringer

2018

Int. J. Mod. Phys. A

Self Cite

View full text Add to dashboard Cite

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.

show abstract

New techniques and results for worldline simulations of lattice field theories

Cited by 6 publications

References 33 publications

Phase unwrapping and one-dimensional sign problems

Phase unwrapping and one-dimensional sign problems

Review on novel methods for lattice gauge theories

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

Contact Info

Product

Resources

About