Interpretation of topologically restricted measurements in lattice σ-models

Abstract

We consider models with topological sectors, and difficulties with their Monte Carlo simulation. In particular we are concerned with the situation where a simulation has an extremely long auto-correlation time with respect to the topological charge. Then reliable numerical measurements are possible only within single topological sectors. The challenge is to assemble such restricted measurements to obtain an approximation for the full-fledged result, which corresponds to the correct sampling over the entire set of configurations. Under certain conditions this is possible, and it provides in addition an estimate for the topological susceptibility χt. Moreover, the evaluation of χt might be feasible even from data in just one topological sector, based on the correlation of the topological charge density. Here we present numerical test results for these techniques in the framework of non-linear σ-models. 2)A continuous deformation of a path does not change Q, hence it remains in the same subset, i.e. in the same topological sector.

Topologically restricted measurements in lattice sigma-models

“…Preliminary results were anticipated in Ref. [8], and Ref. [9] presented before a related study (with different densities) in 2-flavour QCD.…”