2007/09/30 by Matthias Balzer, M. Balzer, Werner Hanke +1
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Theoretical and Computational Physics #cond-mat.str-el #cond-mat.supr-con
paper · pdf · doi:10.1103/physrevb.77.045133
published as Phys. Rev. B 77, 045133 (2008) · 19 pages, 19 figures, v3 with minor corrections, extended discussion
arxiv created 2007/12/14 · openalex publication_date 2008/01/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The variational cluster approach (VCA) is applied to the one-dimensional Hubbard model at zero temperature using clusters (chains) of up to ten sites with full diagonalization and the Lanczos method as cluster solver. Within the framework of the self-energy-functional theory (SFT), different cluster reference systems with and without bath degrees of freedom, in different topologies and with different sets of variational parameters, are considered. Static and one-particle dynamical quantities are calculated for half-filling as a function of U as well as for fixed U as a function of the chemical potential to study the interaction- and filling-dependent metal-insulator (Mott) transition. The recently developed Q-matrix technique is used to compute the SFT grand potential. For benchmarking purposes we compare the VCA results with exact results available from the Bethe ansatz, with essentially exact dynamical density-matrix renormalization-group data, with (cellular) dynamical mean-field theory and full diagonalization of isolated Hubbard chains. Several issues are discussed including convergence of the results with cluster size, the ability of cluster approaches to access the critical regime of the Mott transition, efficiency in the optimization of correlated-site vs bath-site parameters, and of multidimensional parameter optimization. We also study the role of bath sites for the description of excitation properties and as charge reservoirs for the description of filling dependencies. The VCA turns out to be a computationally cheap method which is competitive with established cluster approaches.