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arXiv:cond-mat/9905311 · Journal of Physics Condensed Matter

Breakdown of a magnetization plateau due to anisotropy in Heisenberg mixed-spin chains

Shoji Yamamoto, Tôru Sakai

Published Jan 1, 1999• 16 citations
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Abstract

We discuss the critical behaviour of the spin-(1,½) Heisenberg ferrimagnetic chain in a magnetic field, whose magnetization curve exhibits a plateau at a third of the full magnetization. A bond alternation stabilizes the massive state, whereas an exchange anisotropy causes the breakdown of the plateau and the onset of a gapless spin-fluid state, where the transition, lying in the XY but ferromagnetic region, is of Kosterlitz-Thouless type. In order to elucidate significant quantum effects, we investigate the model of the classical version as well.

DOI
10.1088/0953-8984/11/26/318

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•Dec 20, 2022•0 citations
We discuss the critical behaviour of the spin-(1,½) Heisenberg ferrimagnetic chain in a magnetic field, whose magnetization curve exhibits a plateau at a third of the full magnetization. A bond alternation stabilizes the massive state, whereas an exchange anisotropy causes the breakdown of the plateau and the onset of a gapless spin-fluid state, where the transition, lying in the XY but ferromagnetic region, is of Kosterlitz-Thouless type. In order to elucidate significant quantum effects, we investigate the model of the classical version as well.
We numerically investigate the critical behavior of the spin-(1,12)(1,\frac{1}{2})(1,21​) Heisenberg ferrimagnet with anisotropic exchange coupling in a magnetic field. A quantized magnetization plateau as a function of the field, appearing at a third of the saturated magnetization, is stable over the whole antiferromagnetic coupling region. The plateau vanishes in the ferromagnetic coupling region via the Kosterlitz-Thouless transition. Comparing the quantum and classical magnetization curves, we elucidate what are essential quantum effects.
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.
Magnetization curves of the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains are calculated with the help of density-matrix renormalization group method for several quantum spin numbers S=1, 3/2, 2 and 5/2.It is shown that the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains exhibit irrespective of the spin value S exactly one intermediate magnetization plateau, which can be identified with the gapped Lieb-Mattis ferrimagnetic ground state.The magnetization plateau due to the Lieb-Mattis ferrimagnetism breaks down at a quantum phase transition towards the Luttinger spin liquid, which is characterized by a continuous change of the magnetization with the magnetic field until another quantum critical point is reached at the saturation field.
The spin-1/2 Ising-Heisenberg branched chain composed of regularly alternating Ising spins and Heisenberg dimers involving an additional side branching is rigorously solved in a magnetic field by the transfer-matrix approach. The ground-state phase diagram, the magnetization process and the concurrence measuring a degree of bipartite entanglement within the Heisenberg dimers are examined in detail. Three different ground states were found depending on a mutual interplay between the magnetic field and two different coupling constants: the modulated quantum antiferromagnetic phase, the quantum ferrimagnetic phase, and the classical ferromagnetic phase. Two former quantum ground states are manifested in zero-temperature magnetization curves as intermediate plateaus at zero and one-half of the saturation magnetization, whereas the one-half plateau disappears at a triple point induced by a strong-enough ferromagnetic Ising coupling. The ground-state phase diagram and zero-temperature magnetization curves of the analogous spin-1/2 Heisenberg branched chain were investigated using density-matrix renormalization group calculations. The latter fully quantum Heisenberg model involves, besides two gapful phases manifested as zero and one-half magnetization plateaus, gapless quantum spin-liquid phase. The intermediate one-half plateau of the spin-1/2 Heisenberg branched chain vanishes at Kosterlitz-Thouless quantum critical point between gapful and gapless quantum ground states unlike the triple point of the spin-1/2 Ising-Heisenberg branched chain.
At zero temperature, thermal fluctuation is eliminated and phase transitions will occur due to quantum fluctuations that arise from the Heisenberg uncertainty principle. Magnetic insulators, described by the Heisenberg model Hamiltonian, are a known class of physical systems that can undergo quantum phase transitions when submitted to a magnetic field. The magnetic field induces the transition by closing energy gaps through the Zeeman effect. Examples of systems that undergo these transitions are the antiferromagnetic spin-1 chain, the antiferromagnetic spin- 1/2 ladder, the ferrimagnetic mixed spin-1 and spin- 1/2 chains and ladders. The presence of a gap in the energy spectrum with zero magnetic field leads to a magnetization plateau in the magnetization curve. We use the density matrix renormalization group to investigate the magnetization curves of the mixed spin-1 and spin- 1/2 ladder, for antiferromagnetic and ferro- magnetic couplings between the ladder legs J⊥. For J⊥ > 0, the ground-state is ferrimagnetic with the total spin equal to 1/3 of the saturation value, in accord with the Lieb-Mattis theorem. The magnetization curve presents a plateau at total magnetization 1/3 of the saturation value, the 1/3-plateau since the ground state has a gap to excitations that increase the total spin by 1 unit. Decreasing J⊥ below zero, the ground state becomes a singlet, but the 1/3-plateau survives down to a critical value J⊥ = Jc. Given that the gap closes with the magnetization fixed, it is a Kosterlitz-Thouless transition type. To determine Jc, we have made a finite-size scale analysis of the plateau width.