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.

31 pages, 15 figures

References in corpus (9)

• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Structure of Lefschetz thimbles in simple fermionic systems
• Some remarks on Lefschetz thimbles and complex Langevin dynamics
• Monte Carlo calculations of the finite density Thirring model
• 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
• 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