Exact matrix product states at the quantum Lifshitz tricritical point in a spin-1/2 zigzag-chain antiferromagnet with anisotropic $\Gamma$-term

Abstract

Quantum anisotropic exchange interactions in magnets can induce competitions between phases in a different manner from those typically driven by geometrically frustrated interactions. We study a one-dimensional spin-1/2 zigzag chain with such an interaction, $\Gamma$-term, in conjunction with the Heisenberg interactions. We find a ground state phase diagram featuring a multicritical point where five phases converge: a uniform ferromagnet, two antiferromagnets, Tomonaga-Luttinger liquid and a dimer-singlet coexisting with nematic order. This multicritical point is simultaneously quantum tricritical and Lifshitz, and most remarkably, it hosts multi-degenerate ground state wave functions, whose exact form is obtained in the matrix product form and its degeneracy increases in squares of system size.

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• Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction
• Gapped Spin Excitation in Magnetic Ordered State on Yb-Based Zigzag Chain Compound YbAgSe2
• Rigorous lower bound on dynamical exponents in gapless frustration-free systems
• Magnetic-Field Dependence of Paramagnetic Properties Investigated by 63/65Cu-NMR on the Yb Zigzag-Chain Semiconductor YbCuS2
• Ferromagnetic Order of Reduced Magnetic Moments in a Frustrated Sawtooth Chain of the Magnetic Semiconductor ZnYb${}_2$S${}_4$
• Antiferromagnetic Order and Magnetic Frustration in the Honeycomb Heavy-Fermion System Ce(Pt${}_{1-x}$Pd${}_x$)${}_6$Al${}_3$: ${}^{27}$Al and ${}^{195}$Pt NMR Studies
• Exact Fractionalized Ground States in an Extended Spin-1 Kitaev Chain