2002/01/22 by Sandro Sorella, Sorella, Sandro
Physics and Astronomy · #Advanced Condensed Matter Physics #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Strongly Correlated Electrons (cond-mat.str-el) #Superconductivity (cond-mat.supr-con) #Theoretical and Computational Physics #cond-mat.str-el #cond-mat.supr-con
paper · pdf · doi:10.48550/arxiv.cond-mat/0201388
19 pages, 7 colour figures, lecture notes for the Euro Winter School-Kerkrade-NL
arxiv created 2002/01/22 · openalex publication_date 2002/01/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We review a recent approach for the simulation of many-body interacting systems based on an efficient generalization of the Lanczos method for Quantum Monte Carlo simulations. This technique allows to perform systematic corrections to a given variational wavefunction, that allow to estimate exact energies and correlation functions, whenever the starting variational wavefunction is a qualitatively correct description of the ground state. The stability of the variational wavefunction against possible phases, not described at the variational level can be tested by using the ''effective Hamiltonian'' approach. In fact Monte Carlo methods, such as the ''fixed node approximation'' and the ''generalized Lanczos technique'' (Phys. Rev. B 64,024512, 2001) allow to obtain exact ground state properties of an effective Hamiltonian, chosen to be as close as possible to the exact Hamiltonian, thus yielding the most reasonable estimates of correlation functions. We also describe a simplified one-parameter scheme that improve substantially the efficiency of the generalized Lanczos method. This is tested on the t-J model, with a special effort to obtain accurate pairing correlations, and provide a possible non-phonon mechanism for High temperature superconductivity.