The Lefschetz thimble and the sign problem
arXiv:1512.08039
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.
Proceedings of plenary talk at Lattice 2015 conference
References in corpus (15)
- Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
- A Monte Carlo algorithm for simulating fermions on Lefschetz thimbles
- 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
- Complex Langevin Equations and Schwinger-Dyson Equations
- Thimble regularization at work: from toy models to chiral random matrix theories
- Lefschetz-thimble techniques for path integral of zero-dimensional sigma models
- Complex saddle points and the sign problem in complex Langevin simulation
- What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles
- Lefschetz thimble Monte Carlo for many body theories: application to the repulsive Hubbard model away from half filling
- Thimble regularization at work for Gauge Theories: from toy models onwards
- Application of the Lefschetz thimble formulation to the (0+1) dim. Thirring model at finite density
- Thimble regularization at work besides toy models: from Random Matrix Theory to Gauge Theories