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arXiv:2004.10416 · Scientific Reports

Experimental realization of Lieb-Mattis plateau in a quantum spin chain

Hironori Yamaguchi, Taiki Okita, Yoshiki Iwasaki, Yohei Kono, N. Uemoto, Yuko Hosokoshi, Takanori Kida, Takashi Kawakami, Akira Matsuo, Masayuki Hagiwara

Published Jun 8, 2020• 19 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/s41598-020-66336-8

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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.
The search for truly quantum phases of matter is a center piece of modern research in condensed matter physics. Quantum spin liquids, which host large amounts of entanglement-an entirely quantum feature where one part of a system cannot be measured without modifying the rest-are exemplars of such phases. Here, we devise a realistic model which relies upon the well-known Haldane chain phase, i.e. the phase of spin-1 chains which host fractional excitations at their ends, akin to the hallmark excitations of quantum spin liquids. We tune our model to exactly soluble points, and find that the ground state realizes Haldane chains whose physical supports fluctuate, realizing both quantum spin liquid like and symmetry-protected topological phases. Crucially, this model is expected to describe actual materials, and we provide a detailed set of material-specific constraints which may be readily used for an experimental realization.
Abstract The search for truly quantum phases of matter is a center piece of modern research in condensed matter physics. Quantum spin liquids, which host large amounts of entanglement—an entirely quantum feature where one part of a system cannot be measured without modifying the rest—are exemplars of such phases. Here, we devise a realistic model which relies upon the well-known Haldane chain phase, i.e. the phase of spin-1 chains which host fractional excitations at their ends, akin to the hallmark excitations of quantum spin liquids. We tune our model to exactly soluble points, and find that the ground state realizes Haldane chains whose physical supports fluctuate, realizing both quantum spin liquid like and symmetry-protected topological phases. Crucially, this model is expected to describe actual materials, and we provide a detailed set of material-specific constraints which may be readily used for an experimental realization.
We discuss zero-temperature quantum spin chains in a uniform magnetic field, with axial symmetry. For integer or half-integer spin, SSS, the magnetization curve can have plateaus and we argue that the magnetization per site mmm is topologically quantized as $n(S\ensuremath{-}m)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{integer}$ at the plateaus, where nnn is the period of the ground state. We also discuss conditions for the presence of the plateau at those quantized values. For S=3/2S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3/2S=3/2 and m=1/2m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2m=1/2, we study several models and find two distinct types of massive phases at the plateau. One of them is argued to be a ``Haldane gap phase'' for half-integer SSS.
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.
Bipartite Lieb-Mattis ferrimagnetism and the symmetry-protected Haldane phase are paradigmatic mechanisms in quasi-one-dimensional quantum magnets. Both emerge, in distinct regimes, in a mixed-spin 111-12\tfrac{1}{2}21​-12\tfrac{1}{2}21​ Heisenberg trimer chain with antiferromagnetic backbone exchange JJJ and a side spin-12\tfrac{1}{2}21​ coupled to each backbone spin by an exchange JtJ_tJt​ of either sign. Using the density matrix renormalization group, we compute magnetization curves and the entanglement spectrum and entropy. ForJt>0J_t>0Jt​>0 a robust ferrimagnetic plateau forms at magnetization per unit cell m=1m=1m=1, whose multiplet entropy reflects how the conserved magnetization splits between the halves. For Jt<0J_t<0Jt​<0 an m=0m=0m=0 plateau opens and grows with ∣Jt∣|J_t|∣Jt​∣, while the m=1m=1m=1 plateau closes. AsJt→−∞J_t\to-\inftyJt​→−∞ the chain maps onto a spin-111 Heisenberg chain with coupling J/2J/2J/2: the m=0m=0m=0 width Δh≃0.196\Delta h\simeq 0.196Δh≃0.196 matches half the Haldane gap. Exponentially localized spin-12\tfrac{1}{2}21​ edge states and the even-fold degeneracy of the entanglement spectrum confirm the Haldane character of the m=0m=0m=0 phase.
We investigate the extension of pure-state symmetry protected topological phases to mixed-state regime with a strong U(1) and a weak Z2\mathbb{Z}_2Z2​ symmetries in one-dimensional spin systems by the concept of quantum channels. We propose a corresponding topological phase order parameter for short-range entangled mixed states by showing that it is quantized and its distinct values can be realized by concrete spin systems with disorders, sharply signaling phase transitions among them. We also give a model-independent way to generate two distinct phases by various types of translation and reflection transformations. These results on the short-range entangled mixed states further enable us to generalize the conventional Lieb-Schultz-Mattis theorem to mixed states, even without the concept of spectral gaps and lattice Hamiltonians.