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Numerical Methods for Quantum Monte Carlo Simulations of the Hubbard Model

Url: http://www.asianscientist.com/books/wp-content/uploads/2013/06/7291_chap01.pdf
Format: Pdf
Category: Lattice Models
Pages: 110
Clicks: 1024

One of the core problems in materials science is how the interactions between electrons in a solid give rise to properties like magnetism, superconductivity, and metal-insulator transitions. Our ability to solve this central question in quantum statistical mechanics numerically is presently limited to systems of a few hundred electrons. While simulations at this scale have taught us a considerable amount about certain classes of materials, they have very significant limitations, especially for recently discovered materials which have mesoscopic magnetic and charge order. In this paper, we begin with an introduction to the Hub- bard model and quantum Monte Carlo simulations. The Hubbard model is a simple and effective model that has successfully cap- tured many of the qualitative features of materials, such as tran- sition metal monoxides, and high temperature superconductors. Because of its voluminous contents, we are not be able to cover all topics in detail; instead we focus on explaining basic ideas, concepts and methodology of quantum Monte Carlo simulation and leave various part for further study. Parts of this paper are our recent work on numerical linear algebra methods for quantum Monte Carlo simulations.

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