This project aims to develop advanced analytic and numerical methods to analyze the behavior of quantum spin systems near its critical point. Its well known that when system reaches its critical region, small correlations between individual components of the system turn into macroscopic correlations of a large number of particles. As a result most of existing methods of analysis fail in this regime. The system becomes scale invariant (or conformally invariant) in a sense that the whole system behavior is very similar to the behavior of its smaller part. This can be used to formulate a fast converging iterative algorithm which can predict thermodynamic properties of the system with unprecendented accuracy. This algorithm uses a special technique which is called corner transfer matrices method (CTM) originally invented by Prof. R. Baxter. The student will study the method and its modifications and develop a set of analytic and numerical programs suitable for studies of particular interacting quantum systems in 1 or 2 dimensions.

PHYS3001, MATH3351, working knowledge of Mathematica or other programming language and basics of linear algebra