Towards sampling complex actions

Abstract

Path integrals with complex actions are encountered for many physical systems ranging from spin- or mass-imbalanced atomic gases and graphene to quantum chromo-dynamics at finite density to the non-equilibrium evolution of quantum systems. Many computational approaches have been developed for tackling the sign problem emerging for complex actions. Among these, complex Langevin dynamics has the appeal of general applicability. One of its key challenges is the potential convergence of the dynamics to unphysical fixed points. The statistical sampling process at such a fixed point is not based on the physical action and hence leads to wrong predictions. Moreover, its unphysical nature is hard to detect due to the implicit nature of the process. In the present work we set up a general approach based on a Markov chain Monte Carlo scheme in an extended state space. In this approach we derive an explicit real sampling process for generalized complex Langevin dynamics. Subject to a set of constraints, this sampling process is the physical one. These constraints originate from the detailed-balance equations satisfied by the Monte Carlo scheme. This allows us to re-derive complex Langevin dynamics from a new perspective and establishes a framework for the explicit construction of new sampling schemes for complex actions.

29 pages, 9 figures

References in corpus (10)

• The electronic properties of graphene
• 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
• Lattice simulations of real-time quantum fields
• Stochastic quantization at finite chemical potential
• Monte-Carlo simulation of the tight-binding model of graphene with partially screened Coulomb interactions
• Does the complex Langevin method give unbiased results?
• Controlling Complex Langevin simulations of lattice models by boundary term analysis
• Imaginary polarization as a way to surmount the sign problem in ab initio calculations of spin-imbalanced Fermi gases
• Real-time lattice gauge theory actions: unitarity, convergence, and path integral contour deformations

Cited by in corpus (3)

• Complex Langevin approach to interacting Bose gases
• Real-time correlators in 3+1D thermal lattice gauge theory
• Multi-Lattice Sampling of Quantum Field Theories via Neural Operator-based Flows