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Journal of Yangzhou University

Quantum phase transition caused by the frustration and anisotropic effect in the S＝1 ferromagnetic model

Yongjun Liu

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

By using the density matrix renormalization group(DMRG) method,the author investigates the diagram of the one-dimensional frustrated anisotropic ferromagnetic S=1 Heisenberg spin model,in which the nearest neighboring interactions are anisotropic ferromagnetic and the next nearest neighboring exchanges are considerable anti-ferromagnetic.The ground state energy and both the in-plane and out-of-plane spin correlation functions are calculated.Apart from the ferromagnetic phase and the spin-fluid phase in the small frustration region,but in the large frustration region,it is identified that spin correlations decay with a short-range exponential law and an oscillating behavior.The result is different from the previous result for S=1/2.

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By using the density matrix renormalization group(DMRG) method,the author investigates the diagram of the one-dimensional frustrated anisotropic ferromagnetic S=1 Heisenberg spin model,in which the nearest neighboring interactions are anisotropic ferromagnetic and the next nearest neighboring exchanges are considerable anti-ferromagnetic.The ground state energy and both the in-plane and out-of-plane spin correlation functions are calculated.Apart from the ferromagnetic phase and the spin-fluid phase in the small frustration region,but in the large frustration region,it is identified that spin correlations decay with a short-range exponential law and an oscillating behavior.The result is different from the previous result for S=1/2.
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Ground-state properties are studied for the one-dimensional anisotropic spin-1/2 Heisen­ berg magnet with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest­ neighbor interactions, which are assumed to have the same form as regards the anisotropy. The singlet-triplet energy gap, the magnetization, the energy, and the two-spin correlation function in the ground states of finite-size systems of up to 20 spins are calculated exactly. By extrapolating these results, the values of the above quantities at the infinite-size limit are estimated. Special attention is paid to the limiting ground-state phase diagram on the plane of the ratio of the next-nearest-neighbor interaction constant to the nearest-neighbor one versus the anisotropy parameter. It is found that, when the interactions have the XY-type anisotropy, the limiting ground state is in the spin-fluid phase or in the dimer phase depending upon whether the ratio between the interaction constants is smaller or larger than a critical value. It is also found that, when the interactions have the Ising-type anisotropy, a novel phase with unsaturated magnetization appears between the ferromagnetic and (2, 2) antiphase phases in the limiting ground-state phase diagram.
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