Electrically-controlled Magnetic Lattices: A Quantum Monte Carlo Study

We employ stochastic series expansion method of quantum Monte Carlo simulation to investigate the spin configurations of magnetic lattices in graphene,induced by Ruderman-Kittle-Kasuya-Yosida(RKKY)interaction at finite temperature.In this regime,the susceptibility,spin stiffness,and other magnetic properties of the two-dimensional magnetic lattices can be determined with nearest-neighbor coupling(J1),next-nearest-neighbor coupling(J2)and third-nearest-neighbor coupling(J3).Energy and specific heat can be got in our simulation.In Chapters 1,we introduce the research history of graphene and the origin of magnetism.Then we give the structure of this paper.In Chapters 2,the basic theory of classical Monte Carlo is introduced.And show the details of classical Monte Cralo SW algorithm.In Chapters 3,we present the method of Stochastic Series Expansion of Quantum Monte Carlo method in detail,including the theoretical derivation,the basic idea of the algorithm and the code realization of the algorithm.In Chapters 4,we investigate the magnetic lattices on grapheme.Heisenberg model with spin 1/2 was simulated by using the Stochastic Series Expansion Quantum Monte Carlo method.We get the energy,specific heat,susceptibility and magnetization.And the results are discussed.In Chapters 5,we give a survey of main conclusion of the paper and make prospect for using Quantum Monte Carlo to study electrically-controlled magnetic lattices in the future.