Exact Matrix Product States at the Quantum Lifshitz Tricritical Point in a Spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> Zigzag-Chain Antiferromagnet with Anisotropic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Γ</mml:mi></mml:math> Term
H. Saito, Chisa Hotta
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, Γ 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 multidegenerate ground state wave functions with the degeneracy increasing in squares of system size. The exact ground states are obtained in the matrix product form opening wide applications to frustration-free models.