Title: Heisenberg spin chains with additional isotropic three-site exchange interactions
Author(s):

N.B. Ivanov (Institute of Solid State Physics, Bulgarian Academy of Sciences, Tzarigradsko chaussée 72, 1784 Sofia, Bulgaria)

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.

Key words: spin chains, quantum spin phases, three-spin interactions

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