The PhD research project deals with the dynamics of the one-dimensional integrable models, and in particular the Heisenberg XXZ spin chain. These models play a special role in theoretical physics: they are interacting many-body systems that can can be solved with exact analytic methods. Their importance lies in three factors. First of all, the exact solutions can be compared to the results of various approximation methods, thereby testing their scope and their precision. On the other hand, there are real-world materials whose dynamics is described by integrable theories, and the models can also be tailored in modern experiments, for example with ultra-cold atoms. This opens the way to study these strongly interacting, highly entangled quantum states. Finally, the models are also important for various related fields of mathematics and theoretical physics, such as representation theory, quantum groups and quantum algebras, knot theory, string theory, AdS/CFT, etc. The goal of the PhD research is to study open questions regarding the equilibrium and non-equilibrium dynamics of the XXZ spin chain and related models. The actual problems include the solution of the open (half-infinite) spin chain at finite temperature, the calculation of the boundary correlations, and also the study of different non-equilibrium situations (quantum quenches) of the infinite chain. The methods to be applied are mostly theoretic (they include the various forms of the Bethe Ansatz), but simple numerical calculations will be required too. The Department of Theoretical Physics of the Budapest University of Technology and Economics (BME) has been hosting the MTA-BME ''Momentum'' Statistical Field Theory Research Group since 2012 (http://sft.phy.bme.hu/). The members include the group leader Gábor Takács, senior researchers Márton Kormos and Balázs Pozsgay, and BSc, MSc, and PhD students. Although funding for the group will end in June 2017, the group activities will be continued on the basis of various research grants. The PhD student will join this group and take part in the research activities such as group seminars, discussions, conferences, etc.
The candidate is expected to have a general knowledge of quantum mechanics and statistical physics, experience with integrable models is not required. However, it is important to have an interest in mathematical physics and exact solutions, and to have good problem solving skills.