Assembling Kitaev honeycomb spin liquids from arrays of 1D symmetry protected topological phases

TL;DR

This paper proposes a novel construction of Kitaev honeycomb spin liquids using arrays of 1D symmetry protected topological phases, revealing new phases and potential pathways for realization in materials.

Contribution

It introduces a variant of the Kitaev model built from 1D SPT phases, expanding understanding of spin liquids and their experimental realization.

Findings

Phase diagram determined via exact diagonalization

Emergence of SPT building blocks from ladder Hamiltonians

Potential realization in spin-orbit-coupled Mott insulators

Abstract

The Kitaev honeycomb model, which is exactly solvable by virtue of an extensive number of conserved quantities, supports a gapless quantum spin liquid phase as well as gapped descendants relevant for fault-tolerant quantum computation. We show that the anomalous edge modes of 1D cluster-state-like symmetry protected topological (SPT) phases provide natural building blocks for a variant of the Kitaev model that enjoys only a subextensive number of conserved quantities. The symmetry of our variant allows a single additional nearest-neighbor perturbation, corresponding to an anisotropic version of the $\Gamma$ term studied in the context of Kitaev materials. We determine the phase diagram of the model using exact diagonalization. Additionally, we use DMRG to show that the underlying 1D SPT building blocks can emerge from a ladder Hamiltonian exhibiting only two-spin interactions supplemented by a Zeeman field. Our approach may inform a new pathway toward realizing Kitaev honeycomb spin liquids in spin-orbit-coupled Mott insulators.