Topological critical slowing down: variations on a toy model

Understand

Numerical simulations of lattice quantum field theories whose continuum counterparts possess classical solutions with non-trivial topology face a severe critical slowing down as the continuum limit is approached.

• Standard Monte-Carlo algorithms develop a loss of ergodicity, with the system remaining frozen in configurations with fixed topology.
• We analyze the problem in a simple toy model, consisting of the path integral formulation of a quantum mechanical particle constrained to move on a circumference.
• More specifically, we implement for this toy model various techniques which have been proposed to solve or alleviate the problem for more complex systems, like non-abelian gauge theories, and compare them both in the regime of low temperature and in that of very high temperature.