Efficient method for quantum impurity problems out of equilibrium

We introduce an efficient method to simulate the dynamics of an interacting quantum impurity coupled to noninteracting fermionic reservoirs. Viewing the impurity as an open quantum system, we describe the reservoirs by their Feynman-Vernon influence functionals (IFs). The IFs are represented as matrix-product states in the temporal domain, which enables an efficient computation of the dynamics for arbitrary interactions. We apply our method to study quantum quenches and transport in an Anderson impurity model, including highly nonequilibrium setups, and find a favorable performance compared to state-of-the-art methods. The computational resources required for an accurate computation of the dynamics scale polynomially with evolution time, indicating that a broad class of out-of-equilibrium quantum impurity problems are efficiently solvable. This approach will provide additional insights into the dynamical properties of mesoscopic devices and correlated materials.

Automated summary

We propose an efficient method for simulating the dynamics of an interacting quantum impurity coupled to noninteracting fermionic reservoirs. By treating the impurity as an open quantum system, we describe the reservoirs using Feynman-Vernon influence functionals (IFs) represented as matrix-product states in the temporal domain. The method demonstrates favorable performance in studying quantum quenches and transport in an Anderson impurity model, including highly nonequilibrium setups, compared to existing methods. The computational resources needed to accurately compute the dynamics scale polynomially with evolution time, indicating efficient solvability of a broad range of out-of-equilibrium quantum impurity problems. This approach will offer additional insights into the dynamical properties of mesoscopic devices and correlated materials.