Document Type

Article

Publication Date

May 2010

Publication Title

Physical Review E

Volume

81

Issue Number

5

DOI

10.1103/PhysRevE.81.056703

Keywords

Scaling, Inverse, Dynamical, Quantum, Quadratic, Hamiltonians

Disciplines

Astrophysics and Astronomy | Physical Sciences and Mathematics | Physics

Abstract

Dynamical mean-field theory and its cluster extensions provide a very useful approach for examining phase transitions in model Hamiltonians and, in combination with electronic structure theory, constitute powerful methods to treat strongly correlated materials. The key advantage to the technique is that, unlike competing real-space methods, the sign problem is well controlled in the Hirsch-Fye (HF) quantum Monte Carlo used as an exact cluster solver. However, an important computational bottleneck remains; the HF method scales as the cube of the inverse temperature, β. This often makes simulations at low temperatures extremely challenging. We present here a method based on determinant quantum Monte Carlo which scales linearly in β, with a quadratic term that comes in to play for the number of time slices larger than hundred, and demonstrate that the sign problem is identical to HF.

Comments

This article originally appeared in Physical Review E, volume 81, issue 5, 2010, published by the American Physical Society. ©2010 American Physical Society. The article can also be found online at this link.
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