Performance of Complex Langevin Simulation in 0+1 dimensional massive Thirring model at finite density

Abstract

Statistical sampling with the complex Langevin (CL) equation is applied to (0+1)-dimensional Thirring model, and its uniform-field variant, at finite fermion chemical potential $\mu$. The CL simulation reproduces a crossover behavior which is similar to but actually deviating from the exact solution in the transition region, where we confirm that the CL simulation becomes susceptible to the drift singularities, i.e., zeros of the fermion determinant. In order to simulate the transition region with the CL method correctly, we examine two approaches, a reweighting method and a model deformation, in both of which a single thimble with an attractive fixed point practically covers the integration domain and the CL sampling avoids the determinant zeros. It turns out that these methods can reproduce the correct crossover behavior of the original model with using reference ensembles in the complexified space. However, they need evaluation of the reweighting factor, which scales with the system size exponentially. We discuss feasibility of applying these methods to the Thirring model and to more realistic theories.

arXiv comment31 pages, 15 figures

References in corpus (33)

• High density QCD on a Lefschetz thimble?
• The Complex Langevin method: When can it be trusted?
• Complex Langevin: Etiology and Diagnostics of its Main Problem
• Simulating full QCD at nonzero density using the complex Langevin equation
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Gauge cooling in complex Langevin for QCD with heavy quarks
• Controlling complex Langevin dynamics at finite density
• The argument for justification of the complex Langevin method and the condition for correct convergence
• Adaptive stepsize and instabilities in complex Langevin dynamics
• New insights into the problem with a singular drift term in the complex Langevin method
• Monte Carlo study of real time dynamics
• Complex Langevin Dynamics for chiral Random Matrix Theory
• Lefschetz-thimble analysis of the sign problem in one-site fermion model
• Complex Langevin dynamics in the SU(3) spin model at nonzero chemical potential revisited
• Structure of Lefschetz thimbles in simple fermionic systems
• Some remarks on Lefschetz thimbles and complex Langevin dynamics
• An efficient method to compute the residual phase on a Lefschetz thimble
• Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density
• Stability of complex Langevin dynamics in effective models
• Complex Langevin dynamics for dynamical QCD at nonzero chemical potential: a comparison with multi-parameter reweighting
• Lefschetz thimbles and stochastic quantisation: Complex actions in the complex plane
• Monte Carlo calculations of the finite density Thirring model
• Localised distributions and criteria for correctness in complex Langevin dynamics
• Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
• Lefschetz-thimble techniques for path integral of zero-dimensional $O(n)$ sigma models
• Status of Complex Langevin
• Complex saddle points and the sign problem in complex Langevin simulation
• Thirring model at finite density in 2+1 dimensions with stochastic quantization
• Reweighting complex Langevin trajectories
• A study of symmetry breaking in a relativistic Bose gas using the contraction algorithm
• Modifying partition functions: a way to solve the sign problem
• Lefschetz thimble Monte Carlo for many body theories: application to the repulsive Hubbard model away from half filling
• Gauge cooling for the singular-drift problem in the complex Langevin method --- an application to finite density QCD

Cited by in corpus (2)

• Complex Langevin calculations in finite density QCD at large $\mu /T$ with the deformation technique
• Classical Statistical simulation of Quantum Field Theory