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

TL;DR

This paper demonstrates that a three-leg spin-1/2 ladder with frustrated interactions can host a gapless symmetry-protected topological phase, characterized by unique entanglement properties and supported by field-theoretic analysis.

Contribution

It introduces a new gapless SPT phase in an anisotropic triangular-strip model and combines numerical and field-theoretic methods to characterize its topological nature.

Findings

Ground state is a gapless SPT phase with degenerate entanglement spectrum.

Entanglement entropy shows critical behavior, indicating gaplessness.

The phase is a symmetry-protected critical phase, crucially relying on symmetry.

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.