Equilibrium Quantum Impurity Problems via Matrix Product State Encoding of the Retarded Action*

In the 0+1 dimensional imaginary-time path integral formulation of quantum impurity problems, the retarded action encodes the hybridization of the impurity with the bath. We explore the computational power of representing the retarded action as matrix product state (RAMPS).

We focus on the challenging Kondo regime of the single-impurity Anderson model, where non-perturbative strong-correlation effects arise at very low energy scales. We demonstrate that the RAMPS approach reliably reaches the Kondo regime for a range of interaction strengths $U$, with a numerical error scaling as a weak power law with inverse temperature. We investigate the convergence behavior of the method with respect to bond dimension and time discretization by analyzing the error of local observables in the full interacting problem and find polynomial scaling in both parameters.

Our results suggest that the RAMPS approach offers an alternative avenue for exploring quantum impurity problems, thereby setting the stage for future advancements in the method's capability to address more complex quantum impurity scenarios. Overall, our study contributes to the development of efficient and accurate non-wavefunction-based tensor-network methods for quantum impurity problems.