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arXiv:cond-mat/0009481 · Physical review. B, Condensed matter

Magnetization plateaus and phase diagram in polymerized S=1/2 XXZ chains

Wei Chen, Kazuo Hida, B. C. Sanctuary

Published Mar 14, 2001• 11 citations
arXivHTMLPDF

Abstract

The magnetization plateaus of polymerized $S=\frac{1}{2}$ $\mathrm{XXZ}$ chains are studied for general values of p. Two plateau-non-plateau critical lines and one plateau-plateau critical line are found for each value of p. The universality class of the plateau-non-plateau transition belongs to the Brezinskii-Kosterlitz-Thouless type and that of the plateau-plateau transition, to the Gaussian type. The critical points are determined by level spectroscopic analysis of the numerical diagonalization results for $4<~p<~8.$ The multicritical points are calculated using the integral equations based on the Bethe ansatz solution of the $\mathrm{XXZ}$ model. The behavior of multicritical points are analyzed in detail for large p. It is found that the plateau region is enhanced with the increase in periodicity p although the nonplateau region persists as far as p is finite.

DOI
10.1103/physrevb.63.134427

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The magnetization plateaus of polymerized S=12S=\frac{1}{2}S=21​ XXZ\mathrm{XXZ}XXZ chains are studied for general values of p. Two plateau-non-plateau critical lines and one plateau-plateau critical line are found for each value of p. The universality class of the plateau-non-plateau transition belongs to the Brezinskii-Kosterlitz-Thouless type and that of the plateau-plateau transition, to the Gaussian type. The critical points are determined by level spectroscopic analysis of the numerical diagonalization results for 4< p< 8.4<~p<~8.4< p< 8. The multicritical points are calculated using the integral equations based on the Bethe ansatz solution of the XXZ\mathrm{XXZ}XXZ model. The behavior of multicritical points are analyzed in detail for large p. It is found that the plateau region is enhanced with the increase in periodicity p although the nonplateau region persists as far as p is finite.
The plateau-non-plateau transition in the antiferromagnetic-(ferromagnetic)n_{n}n​ polymerized S=1/2S=1/2S=1/2 XXZ chains under the magnetic field is investigated. The universality class of this transition belongs to the Brezinskii-Kosterlitz-Thouless (BKT) type. The critical points are determined by level spectroscopy analysis of the numerical diagonalization data for 4≤p≤134 \leq p \leq 134≤p≤13 where p(≡n+1)p(\equiv n+1)p(≡n+1) is the size of a unit cell. It is found that the critical strength of ferromagnetic coupling decreases with ppp for small ppp but increases for larger enough ppp. It is also found that the plateau for large ppp is wide enough for moderate values of exchange coupling so that it should be easily observed experimentally. This is in contrast to the plateaus for p=3p = 3p=3 chains which are narrow for a wide range of exchange coupling even away from the critical point.
We study the breakdown of the magnetization plateau at the magnetization M = M S /3 ( M S is the saturation magnetization) of the S = 1/2 anisotropic spin chain with ferromagnetic-ferromagnetic-antiferromagnetic interactions. We consider the model with the isotropic ferromagnetic (trimer) coupling J F , and anisotropic antiferromagnetic coupling ( J x = J y = J AF and J z = J AF ). For the limit of large J F / J AF , the model is equivalent to the S = 3/2 XXZ chain with the exchange anisotropy . There is a phase transition between the plateau (small- ) and the no-plateau (large- ) regions. This phase transition is of the Berezinskii-Kosterlitz-Thouless type, and we determine the phase boundary from the numerical diagonalization data. For = 1, in particular, the phase transition between the plateau and the no-plateau regions occurs at the point c = 15.4.
We study the plateau of the magnetization curve at M = M s /3 ( M s is the saturation magnetization) of the S = ½ trimerized XXZ spin chain. By examining the level crossing of low-lying excitations obtained from the numerical diagonalization, we precisely determine the phase boundary between the plateau state and the no-plateau state on the - t plane, where denotes the XXZ anisotropy and t the magnitude of the trimerization. This quantum phase transition is of the Berezinskii-Kosterlitz-Thouless type.
One-dimensional S=1S=1S=1 XXZ\mathrm{XXZ}XXZ chains with uniaxial single-ion-type anisotropy are studied by numerical exact diagonalization of finite-size systems. The numerical data are analyzed using conformal field theory, the level spectroscopy, phenomenological renormalization-group, and finite-size scaling method. We thus present a quantitatively reliable ground-state phase diagram of this model. The ground states of this model contain the Haldane phase, large-D phase, N\'eel phase, two XY\mathrm{XY}XY phases, and the ferromagnetic phase. There are four different types of transitions between these phases: the Brezinskii-Kosterlitz-Thouless-type transitions, the Gaussian-type transitions, the Ising-type transitions, and the first-order transitions. The locations of these critical lines are accurately determined.
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The magnetization plateaus of frustrated Kondo necklace model have been studied with use of the bosonization technique and level spectroscopy method. It is shown that the model may show three phases (dimer plateau, Néel plateau and Tomonaga-Luttinger liquid phases) due to competitions among Ising anisotropy Δ, the nearest and next nearest neighbor exchange interactions J1, J2. It is shown from bosonization technique that quantum transition between the dimer and Néel plateaus is Gaussian type, while the transition from one of these plateau phases to Tomonaga-Luttinger phase is Brezinskii-Kosterlitz-Thouless type. The phase diagram is constructed on the Δ-J2/J1 plane with use of level spectroscopy method, under the condition that the system has a half of the saturation magnetization.