A periodic cluster perturbation theory is used to investigate a fermion system. The theory is based on the dynamical cluster approximation with relaxing of self-consistency. Within the periodic cluster perturbation theory the self-energy is approximated by the self-energy of an isolated cluster with periodic boundary conditions. The small parameter of the theory is of order of $1∕{L}_{c}$ , where ${L}_{c}$ is the linear size of the cluster. It is found that within the periodic cluster perturbation theory, quantities averaged over the cluster converge rapidly with corrections $O(1∕{L}_{c}^{2})$ , whereas within the cluster perturbation theory, they converge with corrections $O(1∕{L}_{c})$ .A periodic cluster perturbation theory is used to investigate a fermion system. The theory is based on the dynamical cluster approximation with relaxing of self-consistency. Within the periodic cluster perturbation theory the self-energy is approximated by the self-energy of an isolated cluster with periodic boundary conditions. The small parameter of the theory is of order of $1∕{L}_{c}$, where ${L}_{c}$ is the linear size of the cluster. It is found that within the periodic cluster perturbation theory, quantities averaged over the cluster converge rapidly with corrections $O(1∕{L}_{c}^{2})$, whereas within the cluster perturbation theory, they converge with corrections $O(1∕{L}_{c})$.

Physical Review BOct 25, 20063 citations

Quantum periodic cluster methods for strongly correlated electron systems

Tran Minh-Tien

Quantum periodic cluster methods for strongly correlated electron systems are reformulated and developed. The reformulation and development are based on a canonical transformation which periodizes the fermions in the cluster space. The dynamical cluster approximation and the cellular dynamical mean field theory are related each other through the canonical transformation. A cluster perturbation theory with periodic boundary conditions is developed. It is found that the periodic cluster perturbation theory converges rapidly with corrections $\mathcal{O}(1/L_c^2)$ , where $L_c$ is the linear size of the clusters, whereas the ordinary cluster perturbation theory converges with corrections $\mathcal{O}(1/L_c)$ .Quantum periodic cluster methods for strongly correlated electron systems are reformulated and developed. The reformulation and development are based on a canonical transformation which periodizes the fermions in the cluster space. The dynamical cluster approximation and the cellular dynamical mean field theory are related each other through the canonical transformation. A cluster perturbation theory with periodic boundary conditions is developed. It is found that the periodic cluster perturbation theory converges rapidly with corrections $\mathcal{O}(1/L_c^2)$, where $L_c$ is the linear size of the clusters, whereas the ordinary cluster perturbation theory converges with corrections $\mathcal{O}(1/L_c)$.

arXiv:cond-mat/0602615Feb 27, 20060 citations

Perturbation Theory

Jochen Pade

Undergraduate lecture notes in physicsNov 7, 20130 citations

1∕{L}_{c}

, where

{L}_{c}

is the linear size of the cluster. It is found that within the periodic cluster perturbation theory, quantities averaged over the cluster converge rapidly with corrections

O(1∕{L}_{c}^{2})

, whereas within the cluster perturbation theory, they converge with corrections

O(1∕{L}_{c})

\mathcal{O}(1/L_c^2)

, where

L_c

is the linear size of the clusters, whereas the ordinary cluster perturbation theory converges with corrections

\mathcal{O}(1/L_c)