2014/12/31 by Takuya Kanazawa, Yuya Tanizaki
Physics and Astronomy · #Black Holes and Theoretical Physics #Physics of Superconductivity and Magnetism #Theoretical and Computational Physics #hep-lat #hep-th
paper · pdf · doi:10.1007/jhep03(2015)044
published as JHEP03(2015)044 · 37 pages, 17 figures. v2: minor changes, the version to appear in JHEP
arxiv created 2015/02/18 · openalex publication_date 2015/03/01 · arxiv updated 2015/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The Picard-Lefschetz theory offers a promising tool to solve the sign problem in QCD and other field theories with complex path-integral weight. In this paper the Lefschetz-thimble approach is examined in simple fermionic models which share some features with QCD. In zero-dimensional versions of the Gross-Neveu model and the Nambu-Jona-Lasinio model, we study the structure of Lefschetz thimbles and its variation across the chiral phase transition. We map out a phase diagram in the complex four-fermion coupling plane using a thimble decomposition of the path integral, and demonstrate an interesting link between anti-Stokes lines and Lee-Yang zeros. In the case of nonzero mass, it is shown that the approach to the chiral limit is singular because of intricate cancellation between competing thimbles, which implies the necessity to sum up multiple thimbles related by symmetry. We also consider a Chern-Simons theory with fermions in 0 + 1-dimension and show how Lefschetz thimbles solve the complex phase problem caused by a topological term. These prototypical examples would aid future application of this framework to bona fide QCD.