Understanding quantum gravity is one of the most important unsolved problems in high energy theoretical physics. The past six years have seen remarkable progress in this field in terms of exactly solvable holographic lower dimensional models, starting with the SYK model and 2d JT gravity. In this project, we aim to understand this class of solvable models better, with two goals in mind. Firstly, we want to characterize how large ...
Due to the exponential scaling of the problem, larger quantum many-body systems are not exactly solvable on present-day computers. DMRG (density matrix renormalization group) is one of the most successful methods to solve these systems approximately. The proposed project aims to extend DMRG through development of perturbative techniques on top of an active-space matrix product state to increase the accuracy.
The way how collective behaviour is developed within a particular many-body system, remains an open question. This project will address this problem twofold. A first part will embody the study of exactly-solvable Richardson-Gaudin systems for nuclear shell-model calculations. A second part will be devoted to the further development of the Collective model in the Cartan-Weyl basis.