Estimating the Density of States of Frustrated Spin Systems

2018. No. 1808.04340.

Barash L., Marshall J., Weigel M., Hen I.

Estimating the density of states of systems with rugged free energy landscapes is a notoriously difficult task of the utmost importance in many areas of physics ranging from spin glasses to biopolymers to quantum computing. Some of the standard approaches suffer from a spurious convergence of the estimates to metastable minima, and these cases are particularly hard to detect. Here, we introduce a sampling technique based on population annealing enhanced with a multi-histogram analysis and report on its performance for spin glasses. We demonstrate its ability to overcome the pitfalls of other entropic samplers, resulting in some cases in orders of magnitude scaling advantages that can result in the uncovering of new physics. To do that we devise several schemes that allow us to achieve exact counts of the degeneracies of the tested instances.

Keywords: квантовые вычисления, спиновые стекла, phase transitions, фазовые переходы, quantum computation, density of states, плотность состояний, Statistical mechanics, статистическая механика, entropic sampling methods, spin glasses, методы энтропийной выборки