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

TL;DR

This study investigates the complex phase diagram of a frustrated spin-1/2 XXZ chain with bond alternation, revealing multiple gapped phases, the effects of magnetic fields, and potential relevance to specific quantum materials.

Contribution

It provides a detailed analysis of the phase transitions and order parameters in a dimerized frustrated spin chain using DMRG and bosonization, highlighting new phases induced by bond alternation and magnetic fields.

Findings

Identification of four gapped phases with distinct dimer orders.

Discovery of a field-induced transition to a VC-Neel-dimer phase.

Stability of the VCND phase under high magnetic fields.

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.