Phase transitions in driven-dissipative many-body quantum systems

Subtitle:Gutzwiller quantum trajectories and a study of mean-field validity

Open quantum systems have become subject of intense research in the latest years due to technological and experimental advances and their potential for quantum information applications. An open quantum system is subject to an interaction with its environment with which it can exchange e.g. particles or energy. Usually this type of interaction results in a dissipation of the system’s energy into the environment and a drive is needed to compensate for this loss. The competition of these driving and dissipation processes can result in very interesting physical phenomena, such as phase transitions, that are markedly distinct from their equilibrium counterparts. Subsequently, the theoretical interest in these systems has burgeoned and a plethora of theoretical techniques have been developed. Due to the scarcity of analytical solutions, these are mainly based on numerical simulations. A crucial obstacle to be overcome is the exponential growth in computational resources that is required in a numerically exact approach. As a result, there is a clear need for the development of approximative methods and methods that exploit the symmetries that are present in these systems to allow for a more efficient numerical study. In this thesis the properties of driven-dissipative quantum systems are studied by resorting to approximative methods based on a factorisation of the system’s state as well as exact simulation methods based on the exploitation of permutational symmetries. Additionally, an efficient method to extract the properties of these systems in the long time limit has been introduced. Our techniques have been applied to the study of the properties of the dissipative XYZ Heisenberg model as well as those of the driven-dissipative Bose Hubbard model, shedding light on the importance of quantum and classical correlations in these systems.

Publication year:2021

Keywords:Doctoral thesis

Accessibility:Open