Recent advances in determinant quantum Monte Carlo

Abstract

Determinant quantum Monte Carlo is a method for studying magnetic, transport and thermodynamic properties of interacting fermions on a lattice. It is widely used to explore the physics of strongly correlated quantum systems, from cuprate superconductors to ultracold atoms trapped on optical lattices. This paper contains a description of recent algorithmic advances in the determinant quantum Monte Carlo technique. Focus will be on algorithms developed for hybrid multicore processor and GPU platforms. The resulting speed-up of the simulations will be quantified. Simulations’ results will also be presented, with an emphasis on physical quantities that can now be computed for large numbers of sites.

Keywords:

• Hubbard model
• Mott insulators
• Monte-Carlo
• multilayers

Acknowledgments

This work was supported by the National Science Foundation under grant NSF-PHY-1005503. S. Chiesa, A. Euverte, G.G. Batrouni, and E. Assmann played important roles in testing the codes by applying them to different Hamiltonians and geometries. We also thank B. Gibbs for useful input. S. Gogolenko would also like to thank the Fulbright Program Office in Ukraine and the Institute of International Education for finantial support during this study.

Notes

Since the chemical potential term is diagonal, it is often combined with the last term of Equation (8(8) ). Therefore contains the hopping matrix elements only.

When the spin degree of freedom is included in the formulation, the occupation number basis consists of direct product of basis state at different spin sectors. Consequently, the trace becomes a product of traces of each spin component.