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arXiv:1601.05319 · The European Physical Journal B

Alternating-spin S = 3/2 and σ = 1/2 Heisenberg chain with isotropic three-body exchange interactions

Nedko B. Ivanov, Svetozara I. Petrova, Jürgen Schnack

Published May 1, 2016• 7 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2016-70057-y

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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.
The J1-J3 Heisenberg spin models with nearest-neighbor (J1) and additional isotropic three-site (J3) spin interactions remain relatively less explored, although such types of competing exchange terms can naturally emerge from different sources, including the strong-coupling expansion of the multiorbital Hubbard model. Below we present a short survey of the recently published research in this field, the emphasis being on the characteristics of the variety of quantum phases supported by a few generic uniform- and alternating-spin J1-J3 Heisenberg chains. For the reason that the positive (J3>0) three-site couplings tend towards the formation of local quantum dimers, the J1-J3 spin models typically experience some spontaneous dimerization upon increasing J3. Actually, it occurred that the established dimer phases in spin-S J1-J3 Heisenberg chains (S>1/2) serve as complete analogues of the famous gapped Majumdar-Ghosh dimer phase in the spin-1/2 Heisenberg chain with next-nearest-neighbor couplings. The same dimerizations have been observed in the alternating-spin (S,σ) J1-J3 chains (S>σ), provided that the cell spin S+σ= integer, whereas for half-integer cell spin, the local dimer formation produces gapless spin-liquid ground states. The alternating-spin J1-J3 chains also provide some typical examples of spin models supporting the so-called non-Lieb-Mattis magnetic phases.