Frank Pollmann
Technical University of Munich
(Introductory Lecture)
Recent years have seen a great deal of effort to understand quantum thermalization: the question of whether closed quantum systems, evolving under unitary dynamics, reach a state of thermal equilibrium. In my talk, I will discuss how the presence of different conservation laws affects the dynamics of thermalization. First, we investigate the dynamics of quantum entanglement in systems with conservation laws and uncover a qualitative difference between the behavior of the von Neumann entropy and higher Renyi entropies. We argue that the latter generically grow sub-ballistically in systems with diffusive transport. We provide strong evidence for this in both a U(1) symmetric random circuit model and in a paradigmatic non-integrable spin chain, where energy is the sole conserved quantity. Second, we show that systems conserving the dipole moment of an associated global charge exhibit a slow subdiffusive transport. Modelling the time evolution as cellular automata for specific cases of dipole conservation, we numerically find distinct anomalous exponents of the late time relaxation. We explain these findings by analytically constructing a general hydrodynamic model that results in a series of exponents depending on the number of conserved moments, yielding an accurate description of the scaling form of charge correlation functions.