Cluster methods for spin systems
Thomas Pruschke, Andreas Honecker, Stefan Wessel
Spin systems with competing interactions are an active, interesting area of current research. Competing interactions, that is to say “frustration”, can suppress ordering phenomena and thus lead to novel ground states. Moreover, advances in modern material preparation techniques may soon allow to tailor specific spin systems and to control, for example, the degree of frustration. Finally, the calculation of thermodynamic properties of frustrated spin systems is a theoretical and computational challenge: Only very small systems are presently accessible reliably, and hence extrapolations to the thermodynamic limit are virtually impossible.
We propose to devise novel computational schemes for treating spin systems in dimensions D > 1. An approach that has been successful in treating interacting electrons is based on the exact solution of a small system, which is then used to obtain an approximation to the model in the thermodynamic limit via a cluster-perturbation theory. In our project, we want to extend this idea to treat frustrated spin systems. To this end, we intend to employ recent advances in multi-scale methods to set up a perturbative or even variational technique, and to devise new cluster-based quantum Monte Carlo algorithms.