A Monte Carlo Method for Fermion Systems Coupled with Classical Degrees of Freedom

Abstract

A new Monte Carlo method is proposed for fermion systems interacting with classical degrees of freedom. To obtain a weight for each Monte Carlo sample with a fixed configuration of classical variables, the moment expansion of the density of states by Chebyshev polynomials is applied instead of the direct diagonalization of the fermion Hamiltonian. This reduces a cpu time to scale as $O(N_{\dim }^2\log N_{\dim })$ compared to $O(N_{\dim }^3)$ for the diagonalization in the conventional technique; $N_{\dim }$ is the dimension of the Hamiltonian. Another advantage of this method is that parallel computation with high efficiency is possible. These significantly save total cpu times of Monte Carlo calculations because the calculation of a Monte Carlo weight is the bottleneck part. The method is applied to the double-exchange model as an example. The benchmark results show that it is possible to make a systematic investigation using a system-size scaling even in three dimensions within a realistic cpu timescale.

6 pages including 4 figures

Cited by in corpus (46)

• Colossal Magnetoresistant Materials: The Key Role of Phase Separation
• The Kernel Polynomial Method
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Critical Phenomena of Ferromagnetic Transition in Double-Exchange Systems
• Critical Temperature of Ferromagnetic Transition in Three-Dimensional Double-Exchange Models
• Orbital ordering phenomena in $d$- and $f$-electron systems
• Self-Learning Monte Carlo Method in Fermion Systems
• Observation of 3D Heisenberg-like ferromagnetism in single crystal La_{0.875}Sr_{0.125}MnO_3
• Interaction-tuned Anderson versus Mott localization
• Monte Carlo Study of Doping Change and Disorder Effect on Double Exchange Ferromagnetism
• Colossal Magnetoresistance Observed in Monte Carlo Simulations of the One- and Two-Orbital Models for Manganites
• Order N Monte Carlo Algorithm for Fermion Systems Coupled with Fluctuating Adiabatical Fields
• Thermodynamic classification of three-dimensional Kitaev spin liquids
• Low-Energy Excitations of Skyrmion Crystals in a Centrosymmetric Kondo-Lattice Magnet: Decoupled Spin-Charge Excitations and Nonreciprocity
• The Truncated Polynomial Expansion Monte Carlo Method for Fermion Systems Coupled to Classical Fields: A Model Independent Implementation
• Dynamical Switching of Magnetic Topology in Microwave-Driven Itinerant Magnet
• Spontaneous Spatial Inversion Symmetry Breaking and Spin Hall Effect in a Spin-ice Double-exchange Model on a Pyrochlore Lattice
• Green-Function-Based Monte Carlo Method for Classical Fields Coupled to Fermions
• Monte Carlo Algorithm for the Double Exchange Model Optimized for Parallel Computations
• Skyrmion Crystals in the Triangular Kondo Lattice Model
• Double Exchange Models: Self Consistent Renormalisation
• Universality Class of Ferromagnetic Transition in Three-Dimensional Double-Exchange System - O(N) Monte Carlo Study -
• Magnetic Order and Charge Disproportionation in a Spin-ice type Kondo Lattice Model: Large Scale Monte Carlo Study
• Fragility of the A-type AF and CE Phases of Manganites: An Exotic Insulator-to-Metal Transition Induced by Quenched Disorder
• Noncollinear magnetic ordering in a frustrated magnet: Metallic regime and the role of frustration
• Study of the One- and Two-Band Models for Colossal Magnetoresistive Manganites Using the Truncated Polynomial Expansion Method
• Colossal magnetoresistance and quenched disorder in manganese oxides
• Polaronic Aspects of the two-dimensional Ferromagnetic Kondo Model
• Ferromagnetic transition in the double-exchange model on the pyrochlore lattice
• Nonequilibrium charge transport through Falicov-Kimball structures connected to metallic leads
• Noncollinear magnetic ordering in the Shastry-Sutherland Kondo lattice model: Insulating regime and the role of Dzyaloshinskii-Moriya interaction
• Impurity Effect on Ferromagnetic Transition in Double-Exchange Systems
• Non-equilibrium Relaxation Study of Ferromagnetic Transition in Double-Exchange Systems
• A strong coupling theory for electron-mediated interactions in double-exchange models
• Calculation of Dynamical and Many-Body Observables with the Polynomial Expansion Method for Spin-Fermion Models
• Theory of collective excitations in the quadruple-$Q$ magnetic hedgehog lattices
• Polynomial Expansion Monte Carlo Study of Frustrated Itinerant Electron Systems: Application to a Spin-ice type Kondo Lattice Model on a Pyrochlore Lattice
• Magnetic and metal-insulator transitions in coupled spin-fermion systems
• Unsupervised Machine Learning Phase Classification for Falicov-Kimball Model
• Spin-lattice coupling effects in the Holstein double-exchange model
• Application of polynomial-expansion Monte Carlo method to a spin-ice Kondo lattice model
• On the reliability of recent Monte Carlo studies of dilute systems of localized spins interacting with itinerant carriers
• A Study of Parallelizing O(N) Green-Function-Based Monte Carlo Method for Many Fermions Coupled with Classical Degrees of Freedom
• Enhanced ferromagnetism from electron-electron interactions in double exchange type models
• Minimal energy ensemble Monte Carlo for the partition function of fermions coupled to classical fields
• Magnetic properties in the metallic magnets with large anisotropy