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.

arXiv comment10 pages, 5 figures

References in corpus (34)

• Magnetization plateaus in spin chains: ``Haldane gap'' for half-integer spins
• Three-body interactions with cold polar molecules
• Three-spin interactions in optical lattices and criticality in cluster Hamiltonians
• Magnetic Cluster Excitations
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Spin nematics in the bilinear-biquadratic S=1 spin chain
• Rotational modes in molecular magnets with antiferromagnetic Heisenberg exchange
• Phase Diagram of the spin S=1/2 Extended XY model
• Waves in the unseen : theory of spin excitations in a quantum spin nematic
• Quadrupolar Order in Isotropic Heisenberg Models with Biquadratic Interaction
• Octupolar order in the multiple spin exchange model on a triangular lattice
• Thermodynamics of Integrable Chains with Alternating Spins
• Competition between two- and three-sublattice ordering for S=1 spins on the square lattice
• Effective three-body interactions in triangular optical lattices
• Microscopic origin of isotropic non-Heisenberg behavior in highly correlated systems
• Antiferromagnetic spin-S chains with exactly dimerized ground states
• Dynamic properties of the spin-1/2 XY chain with three-site interactions
• Dimerization transitions in spin-1 chains
• Critical Behaviour of integrable mixed spins chains
• Magnetocaloric effect in spin-1/2 $XX$ chains with three-spin interactions
• Spontaneously magnetized Tomonaga-Luttinger liquid in frustrated quantum antiferromagnets
• Phase diagram of a frustrated mixed-spin ladder with diagonal exchange bonds
• Realization of higher Wess-Zumino-Witten models in spin chains
• Spontaneous dimerization, critical lines, and short-range correlations in a frustrated spin-1 chain
• Natural three-qubit interactions in one-way quantum computing
• Magnetism-driven ferroelectricity in spin-1/2 $XY$ chains
• 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
• Dimerizations in spin-$S$ antiferromagnetic chains with three-spin interaction
• Floating, critical and dimerized phases in a frustrated spin-3/2 chain
• Thermodynamics and conformal properties of XXZ chains with alternating spins
• Thermodynamics of antiferromagnetic alternating spin chains
• Phase diagram of the alternating-spin Heisenberg chain with extra isotropic three-body exchange interactions
• Nontrivial ferrimagnetism of the Heisenberg model on the Union Jack strip lattice
• Alternating-spin S=3/2 and sigma=1/2 Heisenberg chain with three-body exchange interactions