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arXiv:1808.00654 · Physical Review Research

Cluster-based Haldane states in spin-1/2 cluster chains

Takanori Sugimoto, Katsuhiro Morita, Takami Tohyama

Published Jun 30, 2020• 10 citations
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Abstract

The authors provide a concept of the Haldane states designed in spin cluster chains, where S=1/2 spins in a cluster strongly interact with each other as compared with inter cluster interactions. As an extension of the Affleck-Kenned-Lieb-Tasaki state, the Haldane states are demonstrated in the spin cluster chains whose cluster consists of not only even but also odd number of spins. Particularly, the Haldane state in the case of an odd number of spins in a cluster is induced by the magnetic field and emerges as a magnetization plateau.

DOI
10.1103/physrevresearch.2.023420

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The authors provide a concept of the Haldane states designed in spin cluster chains, where S=1/2 spins in a cluster strongly interact with each other as compared with inter cluster interactions. As an extension of the Affleck-Kenned-Lieb-Tasaki state, the Haldane states are demonstrated in the spin cluster chains whose cluster consists of not only even but also odd number of spins. Particularly, the Haldane state in the case of an odd number of spins in a cluster is induced by the magnetic field and emerges as a magnetization plateau.
Abstract We have recently proposed a new concept of cluster-based Haldane states supported by an inherent chirality in a triangular spin tube with equivalent inter-cluster interactions. In this state, there appear spin-1/2 degrees of freedom consisting of a real spin and a scalar chirality as edge states. With applying a magnetic field, we can observe approximately a half of magnetization of S = 1/2 spin, i.e., a quarter spin magnetization, due to symmetrization of the real spin and the chirality. Here, we consider effects of discord between two types of inter-cluster interactions, inducing anisotropic biquadratic interactions of effective S = 1 spins. The discord brings the edge magnetization nearer to an exact value of quarter spin magnetization, whereas localization of the edge states becomes worse. These effects are also confirmed in a corresponding spin-1 model.
We investigate the S=2S=2S=2 antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using the numerical exact diagonalization of finite-size clusters and the level spectroscopy analysis. It is found that a magnetization plateau possibly appears at half of the saturation magnetization for some suitable anisotropy parameters. The level spectroscopy analysis indicates that the 1/2 magnetization plateau is formed by two different mechanisms, depending on the anisotropy parameters. The phase diagram of the 1/2 plateau states and some typical magnetization curves are also presented. In addition, the biquadratic interaction is revealed to enhance the plateau induced by the Haldane mechanism.
The S=12S=\frac{1}{2}S=21​ chain-boundary excitations occurring in the Haldane phase of S=1S=1S=1 antiferromagnetic spin chains are investigated. The bilinear-biquadratic Hamiltonian is used to study these excitations as a function of the strength of the biquadratic term, \ensuremath{\beta}, between $\ensuremath{-}1<~\ensuremath{\beta}<~1.$ At the Affleck-Kennedy-Lieb-Tasaki point, $\ensuremath{\beta}=\ensuremath{-}\frac{1}{3},$ we show explicitly that these excitations are localized at the boundaries of the chain on a length scale equal to the correlation length $\ensuremath{\xi}=1/\mathrm{ln}3$, and that the on-site magnetization for the first site is 〈S1z〉=23.〈{S}_{1}^{z}〉=\frac{2}{3}.〈S1z​〉=32​. Applying the density matrix renormalization group we show that the chain-boundary excitations remain localized at the boundaries for $\ensuremath{-}1<\ensuremath{\beta}<1.$ As the two critical points \ensuremath{\beta}=\ifmmode\pm\else\textpm\fi{}1 are approached the size of the S=12S=\frac{1}{2}S=21​ objects diverges and their amplitude appears to vanish.
The Affleck-Kennedy-Lieb-Tasaki state (or Haldane phase) in a spin-1 chain represents a large class of gapped topological paramagnets that host symmetry-protected gapless excitations on the boundary. In this work, we show how to realize this type of featureless spin-1 state on a generic two-dimensional lattice. These states have a gapped spectrum in the bulk, but they support gapless edge states protected by spin rotational symmetry along a certain direction, and they exhibit the spin quantum Hall effect. Using a fermion representation of integer spins, we show a concrete example of such spin-1 topological paramagnets on a kagome lattice, and we suggest a microscopic spin-1 Hamiltonian that may realize it.
The mixed spin-1 and spin-1/2 Heisenberg octahedral chain with regularly alternating monomeric spin-1 sites and square-plaquette spin-1/2 sites is investigated using a variational technique, localized-magnon approach, exact diagonalization, and density-matrix renormalization-group method. The investigated model has, in a magnetic field, an extraordinarily rich ground-state phase diagram, which includes the uniform and cluster-based Haldane phases, two ferrimagnetic phases of Lieb-Mattis type, two quantum spin liquids, two bound magnon crystals, in addition to the fully polarized ferromagnetic phase. The lowest-energy eigenstates in a highly frustrated parameter region belong to flatbands and, hence, low-temperature thermodynamics above the bound magnon-crystal ground states can be satisfactorily described within the localized-magnon approach. The variational method provides exact evidence for the magnon-crystal phase with a character of the monomer-tetramer ground state at zero field, whereas another magnon-crystal phase with a single bound magnon at each square plaquette is found in a high-field region. A diversity of quantum ground states gives rise to manifold zero-temperature magnetization curves, which may involve up to four wide intermediate plateaus at zero, one-sixth, one-third, and two-thirds of the saturation magnetization, two quantum spin-liquid regions, and two tiny plateaus at one-ninth and one-twelfth of the saturation magnetization corresponding to the fragmentized cluster-based Haldane phases.
Abstract Topological properties in material science have recently received tremendous attention, as exemplified by topological insulators. As for quantum spin systems, the Haldane chain with integer spins is the best known example1. The realization of a topological quantum phase in the Haldane chain is an innovative research development related to the 2016 Nobel Prize in Physics. For mixed spin chains composed of two different spins, the appearance of a topologically quantized magnetization plateau is predicted by the Lieb-Mattis theorem2 in combination with the Oshikawa-Yamanaka-Affleck criterion3. However, the actual magnetization plateau in the mixed spin chain has not yet been observed. Here, we present a model compound forming a mixed spin-(1/2, 5/2) chain. We observe a clear Lieb-Mattis plateau and well explain it quantitatively. The present results demonstrate a quantum many-body effect based on quantum topology and provide a new stage in the search for topological properties in condensed matter physics.