Complex Langevin and other approaches to the sign problem in quantum many-body physics

Berger, Casey; Rammelmüller, Lukas; Loheac, Andrew C.; Ehmann, Florian; Braun, Jens; Drut, Joaquín E.

doi:10.1016/j.physrep.2020.09.002

Cited by 64 publications

(70 citation statements)

References 306 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The sign problem is not restricted to quantum gravity, but is also encountered in quantum theories of matter. Several methods have been developed to overcome the sign problem (see e.g., [20,67,68] and references therein). The basic idea of the complex path methods is to deform the integration contour to the complex to reduce the phase fluctuations.…”

Section: Holomorphic Flowmentioning

confidence: 99%

Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects

Jia

2021

Preprint

View full text Add to dashboard Cite

Evaluating gravitational path integrals in the Lorentzian has been a longstanding challenge due to the numerical sign problem. We show that this challenge can be overcome in simplicial quantum gravity. By deforming the integration contour into the complex, the sign fluctuations can be suppressed, for instance using the holomorphic gradient flow algorithm. Working through simple models, we show that this algorithm enables efficient Monte Carlo simulations for Lorentzian simplicial quantum gravity.In order to allow complex deformations of the integration contour, we provide a manifestly holomorphic formula for Lorentzian simplicial gravity. This leads to a complex version of simplicial gravity that generalizes the Euclidean and Lorentzian cases. Outside the context of numerical computation, complex simplicial gravity is also relevant to studies of singularity resolving processes with complex semi-classical solutions. Along the way, we prove a complex version of the Gauss-Bonnet theorem, which may be of independent interest.

show abstract

Section: Holomorphic Flowmentioning

confidence: 99%

Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects

Jia

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…[9] provides a pedagogical review on this method, and ref. [23] is a recent review in the context of the sign problem in quantum many-body physics.…”

Section: Jhep10(2021)186mentioning

confidence: 99%

Complex Langevin dynamics and supersymmetric quantum mechanics

Joseph

Kumar

2021

J. High Energ. Phys.

View full text Add to dashboard Cite

Using complex Langevin method we probe the possibility of dynamical supersymmetry breaking in supersymmetric quantum mechanics models with complex actions. The models we consider are invariant under the combined operation of parity and time reversal, in addition to supersymmetry. When actions are complex traditional Monte Carlo methods based on importance sampling fail. Models with dynamically broken supersymmetry can exhibit sign problem due to the vanishing of the partition function. Complex Langevin method can successfully evade the sign problem. Our simulations suggest that complex Langevin method can reliably predict the absence or presence of dynamical supersymmetry breaking in these one-dimensional models with complex actions.

show abstract

“…An active research community (for a recent review see ref. [20]) is exploring multiple strategies. Among these JHEP08(2021)138 are variants of reweighing, extrapolation from complex parameters and the reformulation of the system of interest in new degrees of freedom unaffected by a sign problem.…”

Section: Motivationmentioning

confidence: 99%

Stable solvers for real-time Complex Langevin

Alvestad

Larsen

Rothkopf

2021

J. High Energ. Phys.

View full text Add to dashboard Cite

This study explores the potential of modern implicit solvers for stochastic partial differential equations in the simulation of real-time complex Langevin dynamics. Not only do these methods offer asymptotic stability, rendering the issue of runaway solution moot, but they also allow us to simulate at comparatively large Langevin time steps, leading to lower computational cost. We compare different ways of regularizing the underlying path integral and estimate the errors introduced due to the finite Langevin time steps. Based on that insight, we implement benchmark (non-)thermal simulations of the quantum anharmonic oscillator on the canonical Schwinger-Keldysh contour of short real-time extent.

show abstract

Complex Langevin and other approaches to the sign problem in quantum many-body physics

Cited by 64 publications

References 306 publications

Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects

Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects

Complex Langevin dynamics and supersymmetric quantum mechanics

Stable solvers for real-time Complex Langevin

Contact Info

Product

Resources

About