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

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.

Figure 1

(Color online) The perturbation order histogram shows the distribution of the typical perturbation order of the diagrams in the simulation. The histogram is peaked around the typical order, which is related to temperature and kinetic energy by $⟨k⟩=\mid E_{\mathit{kin}}\mid ∕T$.

Figure 2

(Color online) The imaginary part of the cluster self-energy ${\Sigma }_{(\pi ,0)}$ on imaginary axis. Temperature $T=0.01t$ is around the critical temperature but still in normal state. At low frequency, the most incoherent self-energy corresponds to optimally doped and not to the underdoped system.

Figure 3

(Color online) The upper panel shows the cluster ${\Sigma }_{(\pi ,0)}$ self-energy on the imaginary axis for both the $t\text{−}J$ (left) and Hubbard (right) model, showing the large scattering rate at optimal doping. The lower panel shows the anomalous self-energy for the same models and doping levels and can be used to locate the optimally doped regime.

Figure 4

(Color online) Projection of the DMFT ground state of alpha and gamma cerium to various atomic configurations of cerium atom. The histograms describe the generalized concept of valence, where the $f$ electron in the solid spends appreciable time in a few atomic configurations. The height of the peak corresponds to the fraction of the time the $f$ electron of the solid spends in one of the eigenstates of the atom, denoted by the total spin $J$ of the atom. We summed up the probabilities for the atomic states, which differ only in the $z$ component of the total spin $J_z$. The $x$ axis indicates the energy of atomic eigenstates in the following way: $\text{energy}(N-1,J)=E_{\mathit{atom}}(N,\text{ground}\text{state})-E_{\mathit{atom}}(N-1,J)$ and $\text{energy}(N+1,J)=E_{\mathit{atom}}(N+1,J)-E_{\mathit{atom}}(N,\text{ground}\text{state})$, where $N$ is between 0 and 2.