Abstract
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.
Highlights
Over the past two decades, it has been established that the Heisenberg spin systems with additional competing interactions — such as longer-range exchange bonds, Dzyaloshinskii-Moria couplings, as well as ring and biquadratic exchange couplings — support a rich variety of spin phases, including the exotic spin ice and spin nematic states, as well as various spin liquids [1]
The interest in such generalized (J1 − J3) isotropic spin models is partially motivated by the belief that the competing 3SE interactions could produce specific phase diagrams, which are not typical of spin systems defined on frustrated lattices and/or with extra well-studied competing interactions such as the longer-ranged exchange bonds and the 2BE interactions
We discussed the quantum phase diagrams of 1D isotropic spin models with extra three-spin interactions, the emphasis being on a few generic spin-1 and alternating-spin (J1 − J3) Heisenberg chains
Summary
Over the past two decades, it has been established that the Heisenberg spin systems with additional competing interactions — such as longer-range exchange bonds, Dzyaloshinskii-Moria couplings, as well as ring and biquadratic exchange couplings — support a rich variety of spin phases, including the exotic spin ice and spin nematic states, as well as various spin liquids [1]. Turning again to the case of Heisenberg spin chains with isotropic 3SE interactions, note that only in the recent few years the quantum phase diagrams of such models with arbitrary strengths (J3) of the 3SE couplings were discussed in the literature. We present a short survey of the recent research in this field, the emphasis being on a few generic 1D Heisenberg spin models with extra 3SE couplings, including the spin-1 and spin-3/2 uniform chains [31,32,33,34,35,36,37], as well as the mixed-spin (1, 1/2) and (3/2, 1/2) chains [38,39,40,41] The interest in such generalized (J1 − J3) isotropic spin models is partially motivated by the belief that the competing 3SE interactions could produce specific phase diagrams, which are not typical of spin systems defined on frustrated lattices and/or with extra well-studied competing interactions such as the longer-ranged exchange bonds and the 2BE interactions. According to the operator identity Si · σj 2 ≡ −Si ·σj/2+S(S+1)/4, the biquadratic terms in this system reduce to bilinear isotropic exchange terms
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