Efficient variational approach to the impurity problem and its application to the dynamical mean-field theory

Abstract

Within the framework of exact diagonalization (ED), we compute the ground state of Anderson impurity problem using the variational approach based on the configuration interaction (CI) expansion. We demonstrate that an accurate ground state can be obtained by iteratively diagonalizing a matrix with the dimension that is less than 10 of the full Hamiltonian. The efficiency of the CI expansion for different problems is analyzed. By way of example, we apply this method to the single-site dynamical mean field theory using ED as the impurity solver. Specifically, to demonstrate the usefulness of this approach, we solve the attractive Hubbard model in the grand-canonical ensemble, where the s-wave superconducting solution is explicitly obtained.

16 pages, one column, double spaced, 2 figures, http://link.aps.org/doi/10.1103/PhysRevB.88.035123

References in corpus (5)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Continuous-time Monte Carlo methods for quantum impurity models
• The numerical renormalization group method for quantum impurity systems
• Nonequilibrium Dynamical Mean Field Theory: an auxiliary Quantum Master Equation approach
• Truncated Configuration Interaction expansions as solvers for correlated quantum impurity models and dynamical mean field theory

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