The SU(2) Chiral Model in an External Field: A Complex Stochastic Process on a Non-Abelian Group

Abstract

The path integral with a complex valued distribution can be evaluated by solving an equivalent stochastic process under some conditions [1,2]. The stochastic evolution of dynamical variables is described by the complex Langevin equation. This opens the new possibility to perform the numerical simulation of the complex action system. The method was tested for a number of toy models [3–6], The results can be described as encouraging, although the problem of convergence to an equilibrium distribution is non-trivial, both from a theoretical and a practical point of view [7]. In this report we present a result of the complex Langevin simulation of the two-dimensional lattice SU(2) chiral model in an external field. This is an interesting test of the complex Langevin equation in a highly non-trivial situation where the solution for the model is known (to some degree of confidence) by the Bethe-ansatz method [8]. A full detail of the following can be found in ref. [9].

Supported by a Nishina Memorial Foundation fellowship.

Presented by S.-K. Yang