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Coexistence of valence-bond formation and topological order in the Frustrated Ferromagnetic $J_1$-$J_2$ Chain

Cliò Efthimia Agrapidis, Stefan-Ludwig Drechsler, Jeroen van den Brink, Satoshi Nishimoto

SciPost Phys. 6, 019 (2019) · published 6 February 2019


Frustrated one-dimensional (1D) magnets are known as ideal playgrounds for new exotic quantum phenomena to emerge. We consider an elementary frustrated 1D system: the spin-$\frac{1}{2}$ ferromagnetic ($J_1$) Heisenberg chain with next-nearest-neighbor antiferromagnetic ($J_2$) interactions. On the basis of density-matrix renormalization group calculations we show the existence of a finite spin gap at $J_2/|J_1|>1/4$ and we find the ground state in this region to be a valence bond solid (VBS) with spin-singlet dimerization between third-neighbor sites. The VBS is the consequence of spontaneous symmetry breaking through order by disorder. Quite interestingly, this VBS state has a Affleck-Kennedy-Lieb-Tasaki-type topological order. This is the first example of a frustrated spin chain in which quantum fluctuations induce gapped topological order.

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Ferromagnetic phases Heisenberg spin chains

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