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

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 a...

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Bibliographic Details
Published inarXiv.org
Main Authors Hidaka, Yuichiro, Furuya, Shunsuke C, Ueda, Atsushi, Tada, Yasuhiro
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 30.10.2022
Subjects
Antiferromagnetism
Chains
Entropy
Ferromagnetism
Ground state
Mathematical models
Perturbation
Physics - Strongly Correlated Electrons
Quantum entanglement
Quantum field theory
Quantum theory
Strip
Symmetry
Topology
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2205.15525