Tempered Lefschetz thimble method and its application to the Hubbard model away from half filling

Abstract

The tempered Lefschetz thimble method (TLTM) is a parallel-tempering algorithm towards solving the numerical sign problem. It tames both the sign and ergodicity problems simultaneously by tempering the system with the flow time of continuous deformations of the integration region. In this article, after reviewing the basics of the TLTM, we explain a new algorithm within the TLTM that enables us to estimate the expectation values precisely with a criterion ensuring global equilibrium and the sufficiency of the sample size. To demonstrate the effectiveness of the algorithm, we apply the TLTM to the quantum Monte Carlo simulation of the Hubbard model away from half filling on a two-dimensional lattice of small size, and show that the obtained numerical results agree nicely with exact values.

arXiv comment7 pages, 4 figures, talk presented at the 37th International Symposium on Lattice Field Theory (Lattice 2019), 16-22 June 2019, Wuhan, China

References in corpus (10)

• High density QCD on a Lefschetz thimble?
• Monte Carlo simulations on the Lefschetz thimble: taming the sign problem
• A Monte Carlo algorithm for simulating fermions on Lefschetz thimbles
• Lefschetz-thimble analysis of the sign problem in one-site fermion model
• Parallel tempering algorithm for integration over Lefschetz thimbles
• Tempered transitions between thimbles
• Applying the tempered Lefschetz thimble method to the Hubbard model away from half-filling
• Implementation of the HMC algorithm on the tempered Lefschetz thimble method
• Emergence of AdS geometry in the simulated tempering algorithm
• Distance between configurations in Markov chain Monte Carlo simulations