Condensed-Matter Physics & Materials Science Seminar

We develop a new impurity solver for the single impurity Anderson model (SIAM), which is based on a non-perturbative recursion technique in a space of operators. Due to the possibility of expanding a self-energy as a continued fraction, which is equivalent to attach a chain to the original lattice sites, we prove that we have an efficient and accurate solver. The method has no peculiar restriction about filling nor temperature and the only approximation is the number of exact levels of continued fraction retained in the expansion. We show how this approach can be advantageously implemented to solve the self-consistent equation of the Dynamical Mean Field Theory (DMTF). We illustrate it with the standard Hubbard model. Depending on how far the recursion process is carried, it is possible, for the 3 first levels of application, to retrieve known approximations (Hartree-Fock, Hubbard I and Hubbard III). When it is applied further, depending on the range of parameters, we are able for instance to reproduce the 3 peaks features and the Fermi liquid regime. All these advantages are promising for the use of this solver in more general cases (quantum dots, multiband).