Vector-spin-chirality order in a dimerized frustrated spin-12chain

Abstract

A frustrated spin-1/2 XXZ chain model comprising a ferromagnetic nearest-neighbor coupling with the bond alternation, J1(1 ± δ) < 0, and an antiferromagnetic second-neighbor exchange coupling J2 > 0 is studied at zero and weak magnetic fields by means of density matrix renormalization group calculations of order parameters, correlation functions and the entanglement entropy as well as an Abelian bosonization analysis. At zero magnetic field, the bond alternation δ > 0 suppresses the gapless phase characterized by a vector-chiral (VC) long-range order (LRO) and a quasi-LRO of an incommensurate spin spiral, whereas this phase occupies a large region in the space of J1/J2 and the easy-plane exchange anisotropy for δ = 0 [S. Furukawa et al., Phys. Rev. Lett. 105, 257205 (2010)]. Then, four gapped phases are found to appear as the exchange anisotropy varies from the SU(2)-symmetric case to the U(1)-symmetric case; the Haldane dimer (D+) phase with the same sign of the x, y-and z-component dimer order parameters, two VC dimer (VCD+/VCD−) phases with the sign of the z-component dimer order parameter being unaltered/reversed, and the even-parity dimer (D−) phase. At small magnetic fields, a field-induced ring-exchange interaction, which is proportional to a staggered scalar chirality and a magnetic flux penetrating the associated triangle, drives a transition from the D− phase into a VC-Neel-dimer (VCND) phase, but not from the D+ phase. This VCND phase is stable up to the large magnetic field at which the Zeeman term closes the spin gap. A possible relevance to Rb2Cu2Mo3O12 is discussed.

Block–spiral magnetism: An exotic type of frustrated order

“…Finally, we make two additional comments: 1) The scenario (long-range effective spin model) described above goes beyond the discussed nonspiral π/2-block case. Changes in the magnetization sector of the long-range FM Hamiltonian lead to modifications in the periodicity of the QLR order (61,62). As a consequence, there are only a few parameters in the effective spin model: the magnetization S z tot related to the filling in the original full multiorbital Hamiltonian and {J2, α} = f (U ) which controls the long-range nature of the system.…”

Quantum disordered vector-spin-chirality state in one dimensional Heisenberg model

“…Hence, a spin excitation gap is required for protecting the vector-spinchirality ordered state without a magnetic spiral LRO. Under these assumptions, the vector-spin-chirality order is found in frustrated spin-1/2 XXZ chain model with suitable nearest-neighbour and next-nearest-neighbour exchange couplings [23].…”

Symmetry-protected topological phase transitions and robust chiral order on a tunable zigzag lattice

“…A vector chiral phase appears but it is very sensitive to the bond alternation. A small difference between J 1 and J 1 will kill the chiral order 19,20 . The effect of large alternation is an interesting question.…”