Lefschetz thimble Monte Carlo for many body theories: application to the repulsive Hubbard model away from half filling

Abstract

Recently, a new method, based on stochastic integration on the surfaces of steepest descent of the action, was introduced to tackle the sign problem in quantum field theories. We show how this method can be used in many body theories to perform fully non-perturbative calculations of quantum corrections about mean field solutions. We discuss an explicit algorithm for implementing our method, and present results for the repulsive Hubbard model away from half-filling at intermediate temperatures. Our results are consistent with those from the recent state of the art cluster dynamical mean field theory calculations.

arXiv comment7 pages, 2 figures

Cited by in corpus (13)

• The argument for justification of the complex Langevin method and the condition for correct convergence
• Lefschetz-thimble analysis of the sign problem in one-site fermion model
• Structure of Lefschetz thimbles in simple fermionic systems
• Some remarks on Lefschetz thimbles and complex Langevin dynamics
• Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density
• Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
• Lefschetz-thimble techniques for path integral of zero-dimensional $O(n)$ sigma models
• Complex saddle points and the sign problem in complex Langevin simulation
• Implementation of the HMC algorithm on the tempered Lefschetz thimble method
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• The Lefschetz thimble and the sign problem
• Performance of Complex Langevin Simulation in 0+1 dimensional massive Thirring model at finite density
• Simulating low dimensional QCD with Lefschetz thimbles