Krylov space time evolution and quantum typicality

Abstract: I will discuss how to perform exact time evolution of many-body wave functions using Krylov space algorithms. This method only relies on a fast matrix vector product of the Hamiltonian (or the evolution operator) and is the only method which can deal with similarly large systems in the regime of strong entanglement, which is generically produced over time. In combination with the concept of quantum typically, which allows us to get rid of traces over operators, this method develops its full power. I will demonstrate this power with the example of how to calculate out of time order correlators in Heisenberg spin chains with short and long range interactions.

condensed matterHEP - theory

Audience: researchers in the topic

Numerical Methods in Theoretical Physics