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

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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Cited by in corpus (14)

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• Topological edge modes and phase transition in the critical fermionic chain with long-range interaction
• Topological metals constructed by sliding quantum wire arrays
• Topological physics in quantum critical systems
• Gauge theory and mixed state criticality
• Incommensurate gapless ferromagnetism connecting competing symmetry-enriched deconfined quantum phase transitions
• Emergence of Kondo-assisted Néel order in a Kondo necklace model
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• Impurity screening by defects in (1+1)$d$ quantum critical systems
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems
• Anomalous Dynamical Scaling at Topological Quantum Criticality