Phase diagram of the quantum spin-1/2 Heisenberg-$\Gamma$ model on a frustrated zigzag chain

Abstract

We investigate the quantum spin-1/2 zigzag chain with frustrated $J_1$-$J_2$ Heisenberg interactions, incorporating additional off-diagonal exchange interactions known as the $\Gamma$ term, both with and without an applied magnetic field. Based on the density-matrix renormalization group calculation, we map out the ground state phase diagram that shows a variety of magnetic and nonmagnetic phases including multicritical points and several exactly solvable points. Upon introducing a finite $\Gamma$ term, we observe the persistent dimer singlet state of the $J_1$-$J_2$ Heisenberg model, sustaining a nonzero spin gap, while also giving rise to a gapless nonmagnetic excitation, manifesting in the substantial zero-energy peak in the nematic dynamical structure factor. This gapless peak-mode remaining almost as a fluctuation to the ground state, induces dilute but robust concentration of nematicity on top of singlets on dimers, which we call the nematic singlet-dimer phase. When the whole nematic excited mode condenses and replaces the singlet, the nematic-dimer phase transforms to the Ising-type ferromagnetic or antiferromagnetic long-range orders that arise from the $\Gamma$ term spontaneously selecting magnetic easy axes. Its orientations dictate the type of magnetic order under geometric frustration effects as predicted by Landau's mean-field theory. These theoretical findings provide insights into the exotic low-temperature phase observed in YbCuS${}_2$, characterized by gapless excitations and seemingly nonmagnetic behavior accompanied by incommensurate correlations.

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Cited by in corpus (6)

• Gapped Spin Excitation in Magnetic Ordered State on Yb-Based Zigzag Chain Compound YbAgSe2
• Magnetic-Field Dependence of Paramagnetic Properties Investigated by 63/65Cu-NMR on the Yb Zigzag-Chain Semiconductor YbCuS2
• Tunable chiral spiral phases in a non-Hermitian Ising-Gamma spin chain
• Ferromagnetic Order of Reduced Magnetic Moments in a Frustrated Sawtooth Chain of the Magnetic Semiconductor ZnYb${}_2$S${}_4$
• Emergent gapless spiral phases and conformal Lifshitz criticality in the cluster Ising model with off-diagonal interactions
• Spin-singlet dimer phase in a frustrated square lattice under a magnetic field