## QUANTUM MONTE CARLO FOR STRONGLY CORRELATED ELECTRONSIn the recent years Quantum Monte Carlo (QMC) methods for lattice models have been considerably improved. By using the systematic convergence of the Lanczos method to the ground state[1] and the recent extension of the so called ''fixed node approximation'' (FN) to lattice models[2], it has been recently possible to define a novel variational approach (SR) with the two important properties of a systematic and accurate computational technique[3]: Hereafter we mention the most important numerical achievements obtained recently:
All these topics have been intensively debated in the literature for at least a decade and have been ''solved numerically'' (i.e. within the limitation of a finite size calculation) by the present approach. [1] E, S, Heeb and T. M. Rice, Europhys. Lett. 82, 3899 (1994). [2] D, F, B. ten Haaf et al., Phys. Rev. B 51, 13039 (1995). [3] S. Sorella, ''Green Function Monte Carlo with Stochastic Reconfiguration'' Phys. Rev. Letters 80, 4558 (1998); ibidem ''Generalized Lanczos algorithm for Variational Monte Carlo'' Phys. Rev. B 64, 024512 (2001). [4] S. Sorella, G. Martins, F. Becca, C. Gazza, L. Capriotti, A. Parola
and E. Dagotto, '' Superconductivity in the 2D t-J model'', Phys. Rev.
Lett. [5] L. Capriotti, Federico Becca, Alberto Parola and Sandro Sorella, ''Resonating Valence Bond Wave Functions for Strongly Frustrated Spin Systems'' Phys. Rev. Lett. 87, 097201 (2001). [6] Federico Becca, Sandro Sorella ''Nagaoka Ferromagnetism in the 2D- infinite U Hubbard model'', Phys. Rev. Lett. 86, 3396 (2001). FUTURE
Our main project in the recent months is to define a computational scheme that satisfies properties (I) and (II) for the realistic Hamiltonian with electron-electron Coulomb interaction, within the Born-Oppenheimer approximation. In principle it is possible to avoid the problem of pseudopotentials and correction schemes to LDA, by defining the realistic Hamiltonian on a lattice with a fixed mesh size , with and increasing computational time , consistent with the requirement (I). ''Large enough'' computer time to obtain a reasonable accuracy in correlation functions (II)- in particular the Born-Oppenheimer forces acting on the nuclei- becomes possible, provided the lattice regularization of the continuous problem is appropriate, namely allowing a lattice mesh , not exceedingly small. Preliminary test cases on simple atoms suggest that an appropriate lattice regularization, defined to be exact (with no dependence) for the Hartee-Fock approximate wavefunction, may fulfill the previous requirement ( with for the exact ground state calculation), even for atoms with large electron number . In this way a reasonable mesh size may be used for an acceptable physical and chemical accuracy, within a computationally possible ''all electron'' calculation. With the proposed approach all the forces acting on the nuclei -within Born-Oppenheimer approximation- can be computed efficiently with QMC schemes, and also long range forces -such as the so important Van der Waals ones- are consistently included. This project requires many human resources for its practical implementation to realistic materials. However it is important to devote much effort to this project, considering its possible applicability to a vast range of materials not yet understood within LDA. For instance Fe2+,or Fe3+ ions in biological environment are so important for enzymatic catalysis but LDA is not even able to reproduce their stable spin configurations. At the moment I am working alone on this project (no students and no postdocs), that however I feel extremely important. If you wish to speed up the future possibilities of QMC schemes for realistic calculations, by helping me with a motivated and qualified collaboration, please do not hesitate to contact me by sorella@sissa.it.
The mechanism of High-temperature superconductivity (HTc) remains until
now an highly debated issue. Our group has contributed to the scientific
discussion (or at least to remove some prejudices) by finding clear numerical
support to the original idea pointed out by P. W. Anderson at the early
stages of HTc. According to this theory (Science 1987) a single-band model,
in presence of strong correlation, can explain not only High-temperature
superconductivity but also all the anomalous properties (linear-T resistivity,
pseudo-gap behavior, anomalous photoemission spectra) measured in these
materials and still unexplained with conventional theories. The basic
point of the theory is that the ground state of the low energy effective
one-band model hamiltonian (t-J or Hubbard at strong coupling) at zero
hole-foping is very well described by a RVB wavefunction, where preformed
Cooper pairs with d-wave symmetry are necessary to describe the singlet
valence bonds of the RVB. In this way it is very natural to expect that,
upon small doping, the experimentally measured d-wave superconductivity
(forbidden by the constraint of no doubly-occupancy at zero hole-doping)
can be established in the t-J model. This has been recently verified numerically
[161], by a newly developed quantum Monte Carlo scheme [125], that so
far represents the most accurate numerical technique for two dimensional
strongly ] correlated electrons. Though our work certainly is not the
definite answer to High-Tc and several questions remain still open, it
represents a promising line of theoretical and numerical investigation
that may allow to understand completely these important phenomena. Recently
in collaboration with V. Anisimov we have also been able to reproduce
many experimental aspects (antiferromagnetic and superconducting zero
temperature transition) of the phase diagram of the most popular HTc compound
La_2 Cu O_4 doped with Sr or Nd, with an ` ab-initio calculation (the
effective J and long range hoppings were computed within LDA+U calculations)
that neglets only the electron-phonon coupling. The inclusion of this
interaction may stabilize true static stripes at commensurate fillings
(e.g. doping 1/8), and is being currently investigated. |