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arXiv · 2205.15525

Gapless symmetry-protected topological phase of quantum antiferromagnets on anisotropic triangular strip

Yuichiro Hidaka·Shunsuke C. Furuya·Atsushi Ueda·Yasuhiro Tada
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Abstract

We study a three-leg spin-1/2 ladder with geometrically frustrated interleg interactions. We call this model an anisotropic triangular-strip (ATS) model. We numerically and field-theoretically show that its ground state belongs to a gapless symmetry-protected topological (SPT) phase. The numerical approach is based on density-matrix renormalization group analyses of the entanglement entropy and the entanglement spectrum. Whereas the entanglement entropy exhibits a critical behavior, the entanglement spectrum is nontrivially degenerate. These entanglement properties imply that the ground state is a gapless topological phase. We investigate the ATS model using a quantum field theory to support the numerical findings. When the frustrated interchain interaction is deemed a perturbation acting on the three spin chains, the frustrated interchain interaction almost isolates the second chain from the other two chains. However, at the same time, the second chain mediates a ferromagnetic interaction between the first and third chains. Therefore, the ground state of the ATS model is a gapless Tomonaga-Luttinger liquid weakly coupled to a spin-1 Haldane chain with irrelevant interactions. Last but not least, we show that the gapless SPT phase of the ATS model is a symmetry-protected critical phase. We point out that the symmetry protection of criticality is essential in characterization of the gapless SPT phase.

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Yuichiro Hidaka, Shunsuke C. Furuya, Atsushi Ueda, Yasuhiro Tada. 2022-10-30. Gapless symmetry-protected topological phase of quantum antiferromagnets on anisotropic triangular strip. https://doi.org/10.1103/physrevb.106.144436

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