The Lefschetz thimble and the sign problem

2015/12/25 by L. Scorzato, Scorzato, Luigi · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Quantum chaos and dynamical systems #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.1512.08039

openalex publication_date 2015/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this talk I review the proposal to formulate quantum field theories (QFTs) on a Lefschetz thimble, which was put forward to enable Monte Carlo simulations of lattice QFTs affected by sign problem. First I will review the theoretical justification of the approach, and comment on some open issues. Then, I will review the algorithms that have been proposed and are being tested to represent and simulate a lattice QFT on a Lefschetz thimble. In particular, I will review the lessons from the very first models of QFTs that have been studied with this approach.

Citations

• Lefschetz thimble Monte Carlo for many body theories: application to the\n repulsive Hubbard model away from half filling
• Analytic Continuation Of Chern-Simons Theory
• Theta Vacua and Boundary Conditions of the Schwinger Dyson Equations
• What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact\n saddles
• Thimble regularization at work for Gauge Theories: from toy models onwards
• Thimble regularization at work besides toy models: from Random Matrix Theory to Gauge Theories
• The Sign Problem, PT Symmetry and Abelian Lattice Duality

Cited by

• Simulating low dimensional QCD with Lefschetz thimbles

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• Quantum field theories on the Lefschetz thimble
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• Taming the sign problem of the finite density Hubbard model via Lefschetz thimbles