Vector-spin-chirality order in a dimerized frustrated spin-1/2 chain

Abstract

A frustrated spin-$1/2$ XXZ chain model comprising a ferromagnetic nearest-neighbor coupling with the bond alternation, $J_1(1\pm \delta )<0$, and an antiferromagnetic second-neighbor exchange coupling $J_2>0$ 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 $\delta >0$ 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 $J_1/J_2$ and the easy-plane exchange anisotropy for $\delta =0$ [S. Furukawa \textit{et al.}, Phys. Rev. Lett. \textbf{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 Rb${}_2$Cu${}_2$Mo${}_3$O${}_{12}$ is discussed.

15 pages, 10 figures

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• Characterizing quantum criticality and steered coherence in the XY-Gamma chain
• Block-spiral magnetism: An exotic type of frustrated order
• Exactly Solvable Points and Symmetry-Protected Topological Phases of Quantum Spins on a Zig-Zag Lattice
• One- and three-dimensional quantum phase transitions and anisotropy in Rb${}_2$Cu${}_2$Mo${}_3$O${}_{12}$
• Cross-over from an incommensurate singlet spiral state with a vanishingly small spin-gap to a valence bond solid state in dimerized frustrated ferromagnetic spin-chains
• Symmetry-protected topological phases and transition in a frustrated spin-$\frac{1}{2}$ XXZ chain
• Roles of easy-plane and easy-axis XXZ anisotropy and bond alternation on a frustrated ferromagnetic spin-$1/2$ chain
• Emergent spin-$1$ Haldane gap and ferroelectricity in a frustrated spin-$1/2$ ladder
• Symmetry-protected topological phase transitions and robust chiral order on a tunable zigzag lattice
• Chiral phases and dynamics of dipoles in triangular optical ladders