Ground State Phase Diagram Of A Nearby Ferromagnetic Spin Model With Anti-ferromagnetic Frustration

Quantum strongly correlated system has been one of the important fields in condensed matter physics.Generally speaking,in comparison with the high-dimensional quantum strongly correlated systems,low-dimensional quantum strongly correlated systems are more likely observed novel physical phenomenon.Frustration,quantum fluctuation,and geometry dimension will bring difficulties to the study of the low-dimensional quantum strongly correlated systems.In the field of low-dimensional quantum strongly correlated systems,a great deal of interest has been concentrated on the frustrated spin system.A lot of man-made materials can be explained by the simplified model for their physical characterization.The most typical numerical methods which can effectively deal with one-dimensional or quasi-one-dimensional quantum spin system are as follows:the exact diagonalization(ED),quantum Monte Carlo(QMC)and density matrix renormalization group(DMRG)methods,and so on.In this thesis,we present a theoretical study on the ground-state properties and the quantum phase transitions of the next-neighboring antiferromagnetic(AF)frustration effect in the quasi-one dimensional ferromagnetic(FM)Heisenberg model by the ED and DMRG.This study was carried out on the basis of the chirality properties and the oscillation behavior of spin correlation.This thesis includes five chapters.In the first chapter,we give a brief introduction to the background of spin-1/2 frustrated ferromagnetic XXZ chain,some experimental examples of the one dimensional spin-1 ferromagnetic chain and the spin correlation oscillation behavior of different models.In the second chapter,we introduce the numerical calculation method,ALPS(Algorithms and Libraries for Physics Simulations)and the related physical order parameters.In chapter III,we focus on the isotropic spin-1 frustrated ferromagnetic Heisenberg model.We investigate the phase diagram of this model from the calculation result of the ground state energy,the behavior of spin correlation function and the chirality order parameter.When 0<??0.25,the ground state is FM state.When 0.25<?<0.4,the ground state is the chiral state,in which the spin correlation shows the cosine modulated incommensurate oscillation behavior with big correlation length and the chiral order parameter has non-zero value.When 0.4??<2,the ground state is the short-ranged incommensurate state(SRO incommensurate),in which the spin correlation shows the incommensurate oscillation behavior with smaller correlation length.While ??2,in the equivalent zigzag ladder model,the antiferromagnetic interaction of intra-chain is bigger than the ferromagnetic interaction of inter-chain,the model turns to two uncoupled antiferromagnetic chain,the ground state is stripe-AF.In chapter IV,we focus on the anisotropic spin-1 frustrated ferromagnetic Heisenberg model.We investigate the phase diagram of this model in the ? and a parameter set,through the calculation result of the behavior of spin correlation and the chirality order parameter.The ground state phase diagram can be divided into three phases:the spin-fluid phase,chiral phase,and SRO incommensurate phase.We indicate the different characteristics of the spin correlation in each phase.In the spin-fluid phase,both the out-of-plane and in-plane spin correlation decay under power law.In the chiral phase,the out-of-plane spin correlation decays exponentially and the in-plane spin correlation shows the oscillation behavior with big correlation length.In the SRO incommensurate phase,the semi-log plots of the in-plane spin correlations always show oscillations with periods.However,the characters of the z-directional spin correlations are dependent on the ? values.If ? is enough small,the semi-log plot of the z-directional spin correlation shows no modulations.Then if ? is not so small,the semi-log plot of the z-directional spin correlation would show periodic oscillations.So in the SRO incommensurate region of the phase diagram,there is a critical disorder point for a certain a.Through calculations of the chiral order parameter,it is found that the chiral phase exists in the moderate frustration region.In the SRO incommensurate phase,we presented the disorder transition line and the Lifshitz transition line through analysis of the z-directional spin correlations and their corresponding spin structure factor.