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arXiv:1407.4606 · The European Physical Journal B

Phase diagram of the alternating-spin Heisenberg chain with extra isotropic three-body exchange interactions

Nedko B. Ivanov, Jörg Ummethum, Jürgen Schnack

Published Oct 1, 2014• 12 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2014-50423-7

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The Heisenberg chain with alternating site spins ( S ,σ) = (1, 1/2) defines a realistic prototype model admitting extra isotropic three-body exchange terms which drive the chain into exotic quantum phases. In this paper, we focus on the non-magnetic part of the phase diagram. Based on numerical density-matrix renormalization group and exact-diagonalization calculations, we demonstrate that the nearest-neighbor three-body interaction stabilizes (i) a critical spin liquid phase described by two Gaussian conformal theories as well as (ii) a critical nematic-like phase characterized by dominant quadrupolar S-spin fluctuations. The emergence of these phases reflects some specific features of the three-body terms such as the promotion of local collinear spin configurations and the enhanced tendency towards nearest- neighbor clustering of the spins.
Additional three-site exchange interactions, naturally arising, e.g., in the strong-coupling expansion of the two-band Hubbard model and in various effective spin Hamiltonians, may stabilize various exotic spin phases which are not typical for the pure Heisenberg models on frustrated lattices and/or with extra biquadratic exchange terms. The reason is hidden in some specific features of the isotropic three-site exchange interactions, such as the promotion of collinear spin configurations as well as the reinforcing tendency towards clustering of the quantum spins on the shortest exchange bonds. As a result, systems with integer and half­integer composite spins in the unit cell might be expected to support different quantum phase diagrams. In this work, we study this phenomenon by comparing the quantum phase diagrams of two Heisenberg chains with extra three-site exchange terms and two different alternating pairs of site spins S and σ [( S , σ) = and ( ], resulting in half-integer and integer cell spins S + σ , respectively.