Stable solvers for real-time Complex Langevin

Alvestad, Daniel; Larsen, Rasmus; Rothkopf, Alexander

doi:10.1007/jhep08(2021)138

Cited by 17 publications

(15 citation statements)

References 51 publications

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“…A study of implicit schemes to numerical evolve the complex Langevin equation is found in ref. [30]. The Lee-Yang theorem states that the magnetic equation of state in the symmetric phase exhibits branch cuts that end at the edge singularities.…”

Section: Methodsmentioning

confidence: 99%

Searching for Yang-Lee zeros in O($N$) models

Attanasio¹,

Bauer²,

Kades³

et al. 2021

Preprint

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Near the second order phase transition point, QCD with two flavours of massless quarks can be approximated by an O(4) model, where a symmetry breaking external field 𝐻 can be added to play the role of quark mass. The Lee-Yang theorem states that the equation of state in this model has a branch cut along the imaginary 𝐻 axis for |𝐼𝑚 [𝐻] | > 𝐻 𝑐 , where 𝐻 𝑐 indicates a second order critical point. This point, known as Lee-Yang edge singularity, is of importance to the thermodynamics of the system. We report here on ongoing work to determine the location of 𝐻 𝑐 via complex Langevin simulations.

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Section: Methodsmentioning

confidence: 99%

Searching for Yang-Lee zeros in O($N$) models

Attanasio¹,

Bauer²,

Kades³

et al. 2021

Preprint

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show abstract

“…The long-term goal of this line of study is to realize genuine real-time simulations of quantum fields on the lattice (see e.g. our work on complex Langevin [18] ). However as an intermediate time goal I see the realization of gauge invariant simulations of the real-time dynamics of classical lattice gauge theory.…”

Section: Pos(lattice2022)385mentioning

confidence: 99%

Towards symmetric discretization schemes via weak boundary conditions

Rothkopf¹

2022

Proceedings of the 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)

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The Szymanzik improvement program for gauge theories is most commonly implemented using forward finite difference corrections to the Wilson action. Central symmetric schemes naively applied, suffer from a doubling of degrees of freedom, identical to the well known fermion doubling phenomenon. And while adding a complex Wilson term remedies the problem for fermions, it does not easily transfer to real-valued gauge fields. In this talk I report on recent progress in formulating symmetric discretization schemes for classical actions of simple one-dimensional problems. They avoid doubling by exploiting the weak imposition of initial/boundary conditions. Inspired by recent work in the field of numerical analysis of partial differential equations, I construct a regularized summation-by-parts finite difference operator using boundary data based on affine coordinates. Application to a classical initial value problems with second order derivatives are presented.

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“…In a previous publication [8] we have shown how to avoid runaway trajectories, by introducing inherently stable solvers to the solution of the complex Langevin dynamics. In contrast to the adaptive step size prescription [9] discussed in the literature, the implicit solvers also provide a novel mechanism to regularize the underlying path integral we wish to simulate.…”

Section: Introductionmentioning

confidence: 99%

Kernel controlled real-time Complex Langevin simulation

2022

Self Cite

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This study explores the utility of a kernel in complex Langevin simulations of quantum real-time dynamics on the Schwinger-Keldysh contour. We give several examples where we use a systematic scheme to find kernels that restore correct convergence of complex Langevin. The schemes combine prior information we know about the system and the correctness of convergence of complex Langevin to construct a kernel. This allows us to simulate up to 2β on the real-time Schwinger-Keldysh contour with the 0 + 1 dimensional anharmonic oscillator using m = 1; λ = 24, which was previously unattainable using the complex Langevin equation.

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Stable solvers for real-time Complex Langevin

Cited by 17 publications

References 51 publications

Searching for Yang-Lee zeros in O($N$) models

Searching for Yang-Lee zeros in O($N$) models

Towards symmetric discretization schemes via weak boundary conditions

Kernel controlled real-time Complex Langevin simulation

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