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Chinese Physics B

Dyson–Maleev theory of an X X Z ferrimagnetic spin chain with single-ion anisotropy

Yu-Ge Chen, Yinxiang Li, Li-Jun Tian, Bin Chen

Published Dec 1, 2018• 1 citation
Publisher

Abstract

We use the mean-field approximation of Dyson–Maleev representation to study an XXZ Heisenberg ferrimagnetic spin chain with single-ion anisotropy. By solving the self-consistent equations with different anisotropies, λ and D respectively, the energy spectrums, internal energy, static susceptibility and specific heat are calculated. Especially, the quantum phase transition of the magnetization plateau induced by single-ion anisotropy D is obtained in the model of the ferrimagnetic spin chain by using Dyson–Maleev mean-field theory.

DOI
10.1088/1674-1056/27/12/127501

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We use the mean-field approximation of Dyson–Maleev representation to study an XXZ Heisenberg ferrimagnetic spin chain with single-ion anisotropy. By solving the self-consistent equations with different anisotropies, λ and D respectively, the energy spectrums, internal energy, static susceptibility and specific heat are calculated. Especially, the quantum phase transition of the magnetization plateau induced by single-ion anisotropy D is obtained in the model of the ferrimagnetic spin chain by using Dyson–Maleev mean-field theory.
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In the present paper, we study the quantum phase transition in the mixed-spin Heisenberg model with the single-ion anisotropy on a bipartite lattice. We prove rigorously that, when the single-ion anisotropy energy DDD is positive, the model has a unique ground state with the total spin-zzz component Sz=0{S}_{z}=0Sz​=0. On the other hand, when the single-ion anisotropy energy is negative and favors the longitudinal spin direction, the global ground state of the system becomes doubly degenerate. Therefore, D=0D=0D=0 is the bifurcation point for the global ground state of the system. Furthermore, we show also that, in the latter case, the global ground state of the mixed-spin Heisenberg chain has the ferrimagnetic long-range order. Our conclusions confirm and generalize the previous results derived by numerical calculations on small size samples.
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The ground-state properties of the spin-(1/2, 1) mixed-spin XXZ chain with single-ion anisotropy (D) are investigated by the infinite time-evolving block decimation (iTEBD) method. A ground-state phase diagram including three phases, i.e., a fully polarized phase, an XY phase and a ferrimagnetic phase, is obtained. The ferrimagnetic phase is found to extend to the regions with (Δ > 1, D > 0) and (Δ < 1, D < 0), where Δ denotes the coupling anisotropy between the localized spins. By the discontinuous behavior of bipartite entanglement, quantum phase transitions (QPTs) between the XY phase and the other two phases are verified to be of the first-order. Furthermore, two constant spontaneous magnetization values (M z = 3/2 and 1/2) are observed in the fully polarized and the ferrimagnetic phases, respectively. In both cases of Δ → +∞ and D → -∞, the ground state tends to the Ising limit. In addition, both the long-range ferromagnetic and antiferromagnetic orders are found to coexist in the whole ferrimagnetic phase.