Combining ordinary and topological finite volume effects for fixed topology simulations

Abstract

In lattice quantum field theories with topological sectors, simulations at fine lattice spacingswith typical algorithms -tend to freeze topologically. In such cases, specific topological finite size effects have to be taken into account to obtain physical results, which correspond to infinite volume or unfixed topology. Moreover, when a theory like QCD is simulated in a moderate volume, one also has to overcome ordinary finite volume effects (not related to topology freezing). To extract physical results from simulations affected by both types of finite volume effects, we extend a known relation between hadron masses at fixed and unfixed topology by additionally incorporating ordinary finite volume effects. We present numerical results for SU(2) Yang-Mills theory.

Metadynamics surfing on topology barriers: the CP N−1 case

“…In the recent literature the problem of very long autocorrelation times and of the theoretical control over the systematic error in numerical simulations has been addressed in a series of papers [2,3,5,[7][8][9][10] and several solutions to the topological critical slowing down have been proposed [4,6,[19][20][21][22][23][24][25].…”

New simulation strategies for lattice gauge theory

“…With the use of open boundary conditions [12], for example, topological charge is no longer quantized and free-energy barriers between the different topological sectors are absent. Physically, changes in topology can occur when topo- 1 It should be noted that the volume dependence of physical observables can be described by analytic formulas (see, e.g., [4,5] for extensions of the results obtained in [3]), and with sufficient data at multiple volumes and multiple fixed topological charge sectors, a direct determination of physical quantities at vanishing theta vacuum is possible. Demonstrations of this strategy are provided in [6].…”