Green-Function-Based Monte Carlo Method for Classical Fields Coupled to Fermions

Abstract

Microscopic models of classical degrees of freedom coupled to non-interacting fermions occur in many different contexts. Prominent examples from solid state physics are descriptions of colossal magnetoresistance manganites and diluted magnetic semiconductors, or auxiliary field methods for correlated electron systems. Monte Carlo simulations are vital for an understanding of such systems, but notorious for requiring the solution of the fermion problem with each change in the classical field configuration. We present an efficient, truncation-free O(N) method on the basis of Chebyshev expanded local Green functions, which allows us to simulate systems of unprecedented size N.

4 pages, 3 figures

References in corpus (10)

• The Kernel Polynomial Method
• Critical Temperature of Ferromagnetic Transition in Three-Dimensional Double-Exchange Models
• Monte Carlo Study of Ferromagnetism in (III,Mn)V Semiconductors
• Hybrid Monte Carlo algorithm for the Double Exchange Model
• A Monte Carlo Method for Fermion Systems Coupled with Classical Degrees of Freedom
• Order N Monte Carlo Algorithm for Fermion Systems Coupled with Fluctuating Adiabatical Fields
• The Truncated Polynomial Expansion Monte Carlo Method for Fermion Systems Coupled to Classical Fields: A Model Independent Implementation
• Universality Class of Ferromagnetic Transition in Three-Dimensional Double-Exchange System - O(N) Monte Carlo Study -
• Considerations on the quantum double-exchange Hamiltonian
• Spin-lattice coupling effects in the Holstein double-exchange model

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