The sign problem and the Lefschetz thimble

Abstract

Recently, we have proposed a novel approach (arxiv:1205.3996) to deal with the sign problem that hinders Monte Carlo simulations of many quantum field theories (QFTs). The approach consists in formulating the QFT on a Lefschetz thimble. In this paper we concentrate on the application to a scalar field theory with a sign problem. In particular, we review the formulation and the justification of the approach, and we also describe the Aurora Monte Carlo algorithm that we are currently testing.

Prepared for the proceedings of XQCD. August 21 - 23, 2012. Washington, DC

References in corpus (3)

• High density QCD on a Lefschetz thimble?
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Method for simulating O(N) lattice models at finite density

Cited by in corpus (12)

• Monte Carlo simulations on the Lefschetz thimble: taming the sign problem
• Hybrid Monte Carlo on Lefschetz Thimbles -- A study of the residual sign problem
• An efficient method to compute the residual phase on a Lefschetz thimble
• Lefschetz thimbles and stochastic quantisation: Complex actions in the complex plane
• Complex Langevin dynamics and other approaches at finite chemical potential
• Metropolis Monte Carlo on the Lefschetz thimble: application to a one-plaquette model
• Complex Saddle Points and Disorder Lines in QCD at finite temperature and density
• Complex saddle points in QCD at finite temperature and density
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Analytical studies of the complex Langevin equation with a Gaussian Ansatz and multiple solutions in the unstable region
• Quantum field theories on the Lefschetz thimble
• Extending complex Langevin simulations to full QCD at nonzero density