New variational method for quantum impurity problems

Quantum impurity models - systems of a few strongly interacting degrees of freedom coupled to a large bath of noninteracting fermions - constitute an important class of problems in condensed matter physics. Despite the small number of interacting modes involved, this class of problems can exhibit rich many-body physics phenomena. Motivated by recent formal results, showing that a coherent superposition of non-orthogonal fermionic Gaussian states is an efficient approximation to the ground states to quantum impurities [Bravyi and Gosset, Comm. Math. Phys., 356 451 (2017)], we present a new practical approach for performing variational calculations for quantum impurity problems. The method uses an approximate projection of imaginary-time equations of motion that decouples the dynamics of each Gaussian state forming the ansatz. As a first application of the method, we calculate properties of the screening cloud of an Anderson impurity and the impurity contribution to the entanglement entropy. We also benchmark our approach using density matrix renormalization group (DMRG) calculations. Finally, we present ongoing work on the study of the ground state of the overscreened multichannel Kondo model, a problem difficult to tackle using conventional numerical tools.