An efficient method for quantum impurity models in and out of equilibrium

Describing a quantum impurity coupled to non-interacting fermionic reservoirs is a paradigmatic problem in quantum many-body physics. We propose an approach to analyze impurity dynamics based on the matrix-product state (MPS) representation of the Feynman-Vernon influence functional (IF) which fully encodes the dynamical influence of the environment. The efficiency of the MPS representation rests on the moderate value of the temporal entanglement (TE) entropy of the IF, viewed as a fictitious “wave function” in the time domain. Once the IF is encoded by a MPS, local correlation functions can be efficiently computed for arbitrary impurity parameters.



In this talk, we use the Single-Impurity Anderson Model as testbed to demonstrate the power of the method:

In equilibrium, we illustrate that it correctly captures the emergence of Kondo physics at large time scales.

Away from equilibrium, we show that transport properties in the steady-state are accessible for a large parameter range.

Last, we expound how the theoretical framework allows for a natural application in dynamical mean-field theory algorithms.