Heisenberg spin chains with additional isotropic three-site exchange interactions

Abstract

The $J_1-J_3$ Heisenberg spin models with nearest-neighbor ($J_1$) and additional isotropic three-site ($J_3$) 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 $J_1-J_3$ Heisenberg chains. For the reason that the positive ($J_3>0$) three-site couplings tend towards the formation of local quantum dimers, the $J_1-J_3$ spin models typically experience some spontaneous dimerization upon increasing $J_3$. Actually, it occurred that the established dimer phases in spin-$S$ $J_1-J_3$ 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 ($S,\sigma$) $J_1-J_3$ chains ($S>\sigma$), provided that the cell spin $S+\sigma =\mathrm{integer}$, whereas for half-integer cell spin, the local dimer formation produces gapless spin-liquid ground states. The alternating-spin $J_1-J_3$ chains also provide some typical examples of spin models supporting the so-called non-Lieb-Mattis magnetic phases.

10 pages, 5 figures

References in corpus (10)

• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Octupolar order in the multiple spin exchange model on a triangular lattice
• Microscopic origin of isotropic non-Heisenberg behavior in highly correlated systems
• Dynamic properties of the spin-1/2 XY chain with three-site interactions
• Magnetocaloric effect in spin-1/2 $XX$ chains with three-spin interactions
• Realization of higher Wess-Zumino-Witten models in spin chains
• Spontaneous dimerization, critical lines, and short-range correlations in a frustrated spin-1 chain
• Exact solution of a spin-1/2 $XX$ chain with three-site interactions in a random transverse field: Influence of randomness on quantum phase transition
• Thermodynamics of antiferromagnetic alternating spin chains
• Phase diagram of the alternating-spin Heisenberg chain with extra isotropic three-body exchange interactions