In theoretical physics most problems can be solved only using certain approximations or numerical methods, and this motivated the study of the so-called integrable models where complete exact solutions can be found despite the models being truly interacting. Examples include statistical physical models, spin chains, and integrable quantum field theories. One model that has been investigated is the famous Heisenberg spin chain. A central topic in the last few years has been the nonequilibrium dynamics, in particular equlibration and thermalization in this model. Whereas a lot is known about the physical properties in equilibrium, there are very few results available about real time evolution. Furthermore, much less is known about the correlation functions and the dynamics of more complicated integrable models, for example spin chains with higher dimensional local spaces. Apart from their relevance to condensed matter physics, these questions are also important for the AdS/CFT correspondence, because the physical quantities in the spin chains (energy levels and overlaps among others) describe certain correlation functions in the N=4 Super Yang-Mills theory.

 

This PhD project aims to study a number of inter-connected open problems in the XXZ chain and related models. We intend to use the Bethe Ansatz and closely related methods, with a certain degree of numerical work involved. We intend to study the dynamical properties of these models, with special attention devoted to the long range deformed models, whose understanding is rather poor at the moment.

 

The research project can be considered pure mathematical physics, but the models describe real world experimental situations, and there is a possibility that some of the calculations will later be confirmed by experiments. The PhD student will work together with the advisor and other members of the BME Statistical Field Theory and the MTA-BME Quantum Correlations research groups.