Quantum Monte Carlo impurity solver for cluster dynamical mean-field theory and electronic structure calculations with adjustable cluster base

Abstract

We generalized the recently introduced impurity solver [P. Werner et al., Phys. Rev. Lett. 97, 076405 (2006)] based on the diagrammatic expansion around the atomic limit and quantum Monte Carlo summation of the diagrams. We present generalization to the cluster of impurities, which is at the heart of the cluster dynamical mean-field methods, and to realistic multiplet structure of a correlated atom, which will allow a high-precision study of actinide and lanthanide based compounds with the combination of the dynamical mean-field theory and band-structure methods. The approach is applied to both the two-dimensional Hubbard and $t\text{−}J$ models within cellular dynamical mean-field method. The efficient implementation of the algorithm, which we describe in detail, allows us to study coherence of the system at low temperature from the underdoped to overdoped regime. We show that the point of maximal superconducting transition temperature coincides with the point of maximum scattering rate, although this optimal doped point appears at different electron densities in the two models. The power of the method is further demonstrated in the example of the Kondo volume collapse transition in cerium. The valence histogram of the dynamical mean-field theory solution is presented, showing the importance of the multiplet splitting of the atomic states.