Edge states and topological orders in the spin liquid phases of star lattice

TL;DR

This paper explores the topological properties and edge states of spin liquid phases in the star lattice, revealing how different phases and flux parameters influence energy structures, Chern numbers, and topological invariants.

Contribution

It provides the first analytical phase diagram of topological orders in chiral spin liquids on the star lattice, linking energy structures with topological invariants.

Findings

Bulk and edge energy structures depend on spin liquid phases and hopping parameters.

Analytical phase diagram of topological orders for chiral spin liquids with flux parameters.

Identification of topological invariance in specific spin liquid phases.

Abstract

A group of novel materials can be mapped to the star lattice, which exhibits some novel physical properties. We give the bulk-edge correspondence theory of the star lattice and study the edge states and their topological orders in different spin liquid phases. The bulk and edge-state energy structures and Chern number depend on the spin liquid phases and hopping parameters because the local spontaneous magnetic flux in the spin liquid phase breaks the time reversal and space inversion symmetries. We give the characteristics of bulk and edge energy structures and their corresponding Chern numbers in the uniform, nematic and chiral spin liquids. In particular, we obtain analytically the phase diagram of the topological orders for the chiral spin liquid states SL[\phi,\phi,-2\phi], where \phi is the magnetic flux in two triangles and a dodecagon in the unit cell. Moreover, we find the topological invariance for the spin liquid phases, SL[\phi_{1},\phi_{2},-(\phi_{1}+\phi_{2})] and SL[\phi_{2},\phi_{1},-(\phi_{1}+\phi_{2})]. The results reveal the relationship between the energy-band and edge-state structures and their topological orders of the star lattice.