Topological Phases of Spin-1/2 Ferromagnetic--Antiferromagnetic Alternating Heisenberg Chains with Alternating Next-Nearest-Neighbour Interaction

TL;DR

This paper investigates topological and trivial spin-gap phases in an alternating Heisenberg chain with next-nearest-neighbor interactions, using entanglement spectra to identify phase boundaries and their insensitivity to interaction strength.

Contribution

It introduces a detailed analysis of topological phases in an alternating Heisenberg chain, employing entanglement spectra to distinguish phases and confirming phase boundary robustness.

Findings

Identification of SPT and trivial phases via entanglement spectra

Phase boundaries are insensitive to the alternation strength

Results align with nonlinear sigma model and exact solutions

Abstract

A series of symmetry-protected topological(SPT) and trivial spin-gap phases in the spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with alternating next-nearest-neighbour interaction are investigated using two kinds of entanglement spectra defined by different divisions of the whole chain. In the case one of the next-nearest-neighbor interaction vanishes, the model reduces to the $\Delta$-chain in which a series of spin-gap phases are found in J. Phys. Soc. Jpn. 77, 044707 (2008). From the degeneracy of the entanglement spectra, these phases are identified as the SPT and trivial phases. It is found that the ground state phases boundaries are insensitive to the strength of the alternation in next-nearest neighbor interaction. These results are consistent with the analysis based on the nonlinear $\sigma$ model and exact solution on the ferromagnetic-nonmagnetic phase boundary.