Controlling the Sign Problem in Finite Density Quantum Field Theory

Abstract

Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analogue. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor signal to noise ratio. We study three alternatives for this integration: the Gaussian approximation, the "telegraphic" approximation, and a novel expansion in terms of theory-dependent moments and universal coefficients. We have tested the methods for QCD at finite densities of heavy quarks. We find that for two of the approximations the results are extremely close - if not identical - to the full answer in the strong sign problem regime.

13 pages, 10 figures

References in corpus (10)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• The density of states in gauge theories
• On the existence of the critical point in finite density lattice QCD
• Complex Langevin dynamics and other approaches at finite chemical potential
• The density of states approach to dense quantum systems
• Anatomy of the sign-problem in heavy-dense QCD
• Density-of-states
• Probability distribution functions in the finite density lattice QCD
• Finite density QCD phase transition in the heavy quark region
• Overcoming strong metastabilities with the LLR method

Cited by in corpus (14)

• Review on novel methods for lattice gauge theories
• Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
• Phase Unwrapping and One-Dimensional Sign Problems
• A density of states approach to the hexagonal Hubbard model at finite density
• Free energy of the self-interacting relativistic lattice Bose gas at finite density
• New DoS approaches to finite density lattice QCD
• Density of states approach for lattice gauge theory with a $\theta$-term
• Reduced critical slowing down for statistical physics simulations
• Real Time Simulations of Quantum Spin Chains: Density-of-States and Reweighting approaches
• Anatomy of a strong residual sign problem on the thimbles
• New canonical and grand canonical DoS techniques for finite density lattice QCD
• Efficient computations of continuous action densities of states for lattice models
• The density of states approach to the sign problem
• Nonanalyticity, sign problem and Polyakov line in Z3-symmetric heavy quark model at low temperature: Phenomenological model analyses