Approximating ground states of impurity models with Gaussian states: applications in Dynamical Mean Field Theory.

In a protocol called Dynamical Mean Field Theory, impurity models are used to treat strongly interacting models, such as the Hubbard model, by self-consistently converging the dynamical properties of the bath with that of the fully interacting Hubbard model. Recently, it has been shown by Bravyi and Gosset that by taking a superposition of a few non-interacting - or Gaussian - states, the ground states of impurity models can be approximated with arbitrary precision. In this talk, I present an algorithm for constructing a subspace of non-orthogonal Gaussian states that approximate the interacting ground state of the impurity model through a classical procedure that variationally minimizes the energy given by the superposition of Gaussian states with respect to the interacting Hamiltonian. Furthermore, I show that this approximation converges in the DMFT protocol similarly to exact diagonalization, allowing for a more numerically efficient way to obtain the phase diagram for the Mott metal-insulator transition. Finally, I describe how dynamical correlation functions necessary for the DMFT protocol can be obtained using quantum computers and the sum of Gaussian states ansatz.