Michael Sonner
The real time evolution of local operators is an important probe into the behavior of quantum system out of equilibrium. Computing the evolution of a local subsystem of a larger many-body system is challenging due to the fast generation of high entanglement in the wavefunction. We encapsulate the effect of the complement of the local subsystem into a discrete version of Feynman and Vernon's influence functional (IF) which we then compress as an MPS. The efficiency of this method relies on a) low entanglement of the IF and b) an algorithm which can efficiently compute the MPS representation of the IF. We demonstrates that the former is true for a variety of systems of physical interest, in particular systems which are dissipative, localized, strongly thermalizing or in proximity to integrable points. For the case of baths composed of free fermions we introduce a procedure which directly yields the MPS representation of the IF. We benchmark our results with established methods and show that we can improve simulation time and accuracy. Finally we discuss how this algorithm can be used as an impurity solver in the context of dynamic mean field theory.