RQMP (CPM) Seminar

Quantum scars and their relations to subspaces with “broken” time evolution operators

Pierre-Gabriel Rozon

Department of Physics
McGill University

In the everyday world, systems like the contents of our coffee mugs always reach an equilibrium state with uniform temperature and concentration if we wait long enough. On this basis, it is intuitive to expect that the steady states of quantum systems (their eigenstates) should be no different. To clarify this relationship between statistical mechanics and quantum physics, the eigenstate thermalization hypothesis (ETH) was developed. It consists of a set of conditions which, if satisfied, guarantee that the use of statistical mechanics to describe the equilibrium properties of the quantum system in question is justified. Empirically, many numerical studies have shown that the ETH is valid when applied to non-integrable models (models that do not possess a prohibitive number of symmetries that would prevent thermalization). However, it has recently been discovered that some non-integrable models can exhibit eigenstates that are not accurately described by statistical mechanics, and these anomalous eigenstates have been termed scarred eigenstates. The mechanisms that are responsible for the emergence of such anomalies are currently the subject of intensive research. In this talk, I will explain how the phenomenon of quantum scars can be understood via the emergence of subspaces characterized by a time evolution operator that differs from the time evolution operator describing the entire Hilbert space. Crucially, this process is not directly related to the symmetries of the Hamiltonian and, therefore, escapes more conventional analyses.