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International Journal of Modern Physics B

Ferrimagnetic order and spontaneous magnetization in a mixed-spin XXZ chain with single-ion anisotropy

Ling Qiang, Guanghua Liu, Guang-Shan Tian

Published Feb 16, 2015• 3 citations
Publisher

Abstract

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.

DOI
10.1142/s0217979215500708

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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.
Employing various numerical methods, we determine the ground-state phase diagram of an ( S , S ') = (1, 2) spin-alternating chain with antiferromagnetic nearest-neighboring exchange interactions and uniaxial single-ion anisotropies. The resulting phase diagram consists of eight kinds of phases including two phases which accompany the spontaneous breaking of the translational symmetry and a ferrimagnetic phase in which the ground-state magnetization varies continuously with the uniaxial single-ion anisotropy constants for the S =1 and S =2 spins. The appearance of these three phases is attributed to the competition between the uniaxial single-ion anisotropies of both spins.
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.
We study quantum phase transitions of a XXZ spin model with spin S = 1/2 and 1 in one dimension. The XXZ spin chain is one of basic models in understanding various one-dimensional magnetic materials. To study this model, we construct infinite-lattice matrix product state (iMPS), which is a tensor product form for a one-dimensional many-body quantum wave function. By using timeevolution- block-decimation method (TEBD) on iMPS, we obtain the ground states of the XXZ model at zero temperature. This method is very delicate in calculating ground states so that we developed a reliable method of finding the ground state with the dimension of entanglement coefficients up to 300, which is beyond the previous works. By analyzing ground-state energies, half-chain entanglement entropies, and entanglement spectrum, we found the signatures of quantum phase transitions between ferromagnetic phase, XY phase, Haldane phase, and antiferromagnetic phase.
The linear real space renormalization group is applied to study alternating spin (1/2,1) chains. The temperature dependences of the specific heat and spin–spin correlation functions for the quantum easy-axis mixed-spin chain are found. The role of single-ion anisotropy is discussed. The phase diagram of Ising spin chains with antiferromagnetic intrachain interactions and weak ferromagnetic interchain interactions is presented. As one expects, the weak interchain coupling leads to antiferrimagnetic long-range order in several chains. The threshold value of single-ion anisotropy below which the system does not exhibit a phase transition is found.
We investigate the ground-state phase diagram for a spin-one quantum Heisenberg antiferromagnetic chain with exchange and single-ion anisotropies in an external magnetic field by using the infinite time-evolving block decimation algorithm to compute the ground-state fidelity per lattice site. We detect all phase boundaries solely by computing the ground-state fidelity per lattice site, with the prescription that a phase transition point is attributed to a pinch point on the ground-state fidelity surface. Furthermore, the results indicate that a magnetization plateau corresponds to a fidelity plateau on the ground-state fidelity surface, thus offering an alternative route for investigating the magnetization processes of quantum many-body spin systems. We characterize all phases by using the local-order parameter, the spin correlation, the momentum distribution of the spin correlation structure factor, and mutual information as a function of the lattice distance. The commensurate and incommensurate phases are distinguished by the mutual information. In addition, the central charges at criticalities are identified by performing a finite-entanglement scaling analysis. The results show that all phase transitions between spin liquids and magnetization plateaus belong to the Pokrovsky-Talapov universality class.
In this paper, we study a generalized anisotropic mixed-spin ferrimagnetic Heisenberg model on an arbitrary bipartite lattice. We prove rigorously that, under some very general conditions, this model has a unique ground state with Sz=0{S}_{z}=0Sz​=0 in the XY\mathrm{XY}XY regime and two degenerate ground states with nonzero magnetization in the Ising regime, respectively. Therefore, the isotropic point of this model is a bifurcation point for its ground states. Furthermore, we also show that, if magnetization of the ground states in the Ising regime is a macroscopic quantity in the thermodynamic limit, then these states have both ferromagnetic and antiferromagnetic long-range order. In other words, they are ferrimagnetically ordered. These conclusions confirm the previous results derived by numerical calculations on small one-dimensional mixed-spin chains.