Study of strongly correlated spin systems using cluster density matrix embedding theory

Density matrix embedding theory (DMET) is a relatively new technique for the calculation of strongly correlated systems. Recently cluster DMET (CDMET) was introduced for the study of spin systems such as the anti-ferromagnetic $J_1-J_2$ model on the square lattice. In this paper, we study the Kitaev-Heisenberg model on the honeycomb lattice using the same techniques. Energy profiles and correlation functions are investigated. We study several types of clusters for the Kitaev-Heisenberg model. We extend the variational ansatz of CDMET using spin-state optimization, yielding improved results. A diagonalization in the tangent space of the variational approach yields information on the excited states and the corresponding spectral functions.