A complex path around the sign problem

Abstract

We review recent attempts at dealing with the sign problem in Monte Carlo calculations by deforming the region of integration in the path integral from real to complex fields. We discuss the theoretical foundations, the algorithmic issues and present some results for low dimensional field theories in both imaginary and real time.

Write up of the talk delivered al Lattice 2017

References in corpus (9)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Structure of Lefschetz thimbles in simple fermionic systems
• Schwinger-Keldysh on the lattice: a faster algorithm and its application to field theory
• Deep Learning Beyond Lefschetz Thimbles
• Monte Carlo calculations of the finite density Thirring model
• Ab initio nuclear thermodynamics
• The Semimetal-Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice
• Finite Density $QE{D}_{1+1}$ Near Lefschetz Thimbles

Cited by in corpus (22)

• Review on novel methods for lattice gauge theories
• Towards grounding nuclear physics in QCD
• Effective Spin Foam Models for Lorentzian Quantum Gravity
• Two-flavor chiral perturbation theory at nonzero isospin: Pion condensation at zero temperature
• Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator
• Cold QCD at finite isospin density: confronting effective models with recent lattice data
• Finite-density gauge correlation functions in QC2D
• Analytical structure of the equation of state at finite density: Resummation versus expansion in a low energy model
• A simple approach towards the sign problem using path optimisation
• High-Energy Phase Diagrams with Charge and Isospin Axes under Heavy-Ion Collision and Stellar Conditions
• Hot QCD at finite isospin density: confronting SU(3) Nambu-Jona-Lasinio model with recent lattice data
• Numerical computations of next-to-leading order corrections in spinfoam large-$j$ asymptotics
• Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects
• Taylor expansions on Lefschetz thimbles (and not only that)
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• Phase structure of the 1+1 dimensional massive Thirring model from matrix product states
• Spinfoams and high performance computing
• 3-dimensional QCD phase diagram with pion condensate in the NJL model
• Time-space duality in 2D quantum gravity
• Positive representations of complex distributions on groups
• Geometric and computational aspects of chiral topological quantum matter
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation