Capturing the long time relaxation dynamics of quantum impurity models by marrying tensor networks and orbital compression

The resolution of quantum impurity problems is crucial for modeling strongly correlated electronic systems, forming the foundation of dynamical mean field theory (DMFT). In this work, we introduce a novel quantum impurity solver that combines a compact representation of these systems in a convenient orbital basis together with the computational capabilities of tensor network methods. By meticulously alternating between temporal evolution and rotations in the orbital basis, our approach enables high accuracy calculations of the real-time dynamics for systems with several hundreds of sites up to large times, applicable to both out-of-equilibrium and stationary scenarios. A key advantage of this method is that the bond dimension remains low and saturates over time, resulting in computational complexity that grows linearly with time after this saturation. We showcase the effectiveness of our method by examining the dynamical formation of the Kondo screening cloud during a quench of the impurity charge, allowing us to capture the complete relaxation process in both time and space.