P1 (2013)

Matrix-product-state-based quantum impurity solvers

Ulrich Schollwöck,  Reinhard M. Noack,  Eric Jeckelmann, and Thomas Pruschke

Quantum impurity problems provide fundamental descriptions of important physical problems such as quantum dots and magnetic impurities in metals, and also play an essential role in dynamical mean-field theory as the effective many-body problem that must be solved. In order to study realistic systems, features such as a generalized parametrization and multiple bands must be included. Efficient numerical quantum impurity solvers are required to treat such problems. In this project, we will develop, optimize, and apply a very promising set of methods, namely matrix-product-state-based quantum impurity solvers, which encompass the density-matrix renormalization group (DMRG) as well as the numerical renormalization group. Recent advances in these methods, especially with regard to the calculation of dynamical, i.e., frequency-dependent response functions, have the potential to significantly improve the effi- ciency and accuracy. Here we will address two topics: (i) the adaptation, development, and optimization of adaptive Chebyshev and Lanczos-vector methods and the correction vector method for the calculation of dynamical response functions for impurity problems within a matrix-product-state-based formulation of the DMRG, and (ii) the extension of the methods to efficiently treat impurities coupled to multiple bands as well as systems containing multiple impurities.