Metadynamics Surfing on Topology Barriers: the $C{P}^{N-1}$ Case

Abstract

As one approaches the continuum limit, $QCD$ systems, investigated via numerical simulations, remain trapped in sectors of field space with fixed topological charge. As a consequence the numerical studies of physical quantities may give biased results. The same is true in the case of two dimensional $C{P}^{N-1}$ models. In this paper we show that metadynamics, when used to simulate $C{P}^{N-1}$, allows to address efficiently this problem. By studying $C{P}^{20}$ we show that we are able to reconstruct the free energy of the topological charge $F(Q)$ and compute the topological susceptibility as a function of the coupling and of the volume. This is a very important physical quantity in studies of the dynamics of the $\theta$ vacuum and of the axion. This method can in principle be extended to $QCD$ applications.

Final version accepted on JHEP. Simulations extended and statistics made homogeneous to ease comparison with HMC

References in corpus (2)

• Critical slowing down and error analysis in lattice QCD simulations
• Topological susceptibility in lattice Yang-Mills theory with open boundary condition

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