Title: High-Quality Preconditioning Techniques for the Multi-Length-Scale Hybrid Quantum Monte Carlo Simulation of the Hubbard Model

Speaker: Ichitaro Yamazaki - University of California, Davis

Date/Time: Tuesday, February 5, 2008, 9:30 am - 10:30 am

Location: CSRI Building, Room 95

Brief Abstract: The hybrid quantum Monte Carlo (HQMC) simulation of the Hubbard model is a powerful tool for studying the electron interactions that characterize the essential properties of materials, such as magnetism and superconductivity. The bottleneck of the HQMC simulation is on the repeated solutions of the underlying multi-length-scale symmetric positive definite (SPD) linear systems of equations. The traditional direct method to solve the linear system is effective for a small number of electrons, but its computational cost scales cubically with the number of electrons. Subsequently, the HQMC simulation with the direct method is limited to hundreds of electrons.

In this talk, we present a new preconditioned iterative solver that demonstrates an optimal linear-scaling complexity of the HQMC simulation for moderately-correlated materials. This allows us to conduct simulations with thousands of electrons. The success of the iterative solver relies on a new high-quality incomplete Cholesky (IC)-based preconditioning technique that we propose. The talk will focus on the analysis and implementation of the preconditioning technique for the solution of multi-length-scale SPD systems. We will also introduce a new software package, ICPACK, to provide a uniform interface for IC-based preconditioners.

CSRI POC: Scott Collis, (505) 284-1123