Majorana corner states in square and Kagome quantum spin liquids

TL;DR

This paper demonstrates that certain quantum spin liquid models can host Majorana excitations localized at corners, behaving as second order topological insulators, which is promising for topological quantum computation.

Contribution

The authors identify two spin models supporting Majorana excitations as second order topological insulators, with one model analytically solvable via Lieb's theorem, and show localization of quasiparticles at corners.

Findings

Majorana excitations can be localized at corners in specific spin models.

One model is analytically solvable using Lieb's theorem.

Localization depends on spin coupling parameters.

Abstract

Quantum spin liquids hosting Majorana excitations have recently experienced renewed interest for potential applications to topological quantum computation. Performing logical operations with reduced poisoning requires to localize such quasiparticles at specific point of the system, with energies that are well defined and inside the bulk energy gap. These are two defining features of second order topological insulators (SOTIs). Here, we show two spin models that support quantum spin liquid phases characterised by Majorana excitations and that behave as SOTIs, one of which is analytically solvable thanks to a theorem by Lieb. We show that, depending on the values of spin couplings, it is possible to localize either fermions or Majorana particles at their corners.