Topological insulator phases of non-interacting particles have been generalized from periodic crystals to amorphous lattices, which raises the question whether topologically ordered quantum many-body phases may similarly exist in amorphous systems? Here we construct a soluble chiral amorphous quantum spin liquid by extending the Kitaev honeycomb model to random lattices with fixed coordination number three. The model retains its exact solubility but the presence of plaquettes with an odd number of sides leads to a spontaneous breaking of time reversal symmetry. We unearth a rich phase diagram displaying Abelian as well as a non-Abelian quantum spin liquid phases with a remarkably simple ground state flux pattern. Furthermore, we show that the system undergoes a finite-temperature phase transition to a conducting thermal metal state and discuss possible experimental realisations.
We study the spin-1/2 Kitaev honeycomb gapless spin liquid in the presence of Stone-Wales-type local lattice defects with odd-sided plaquettes. While the clean Kitaev model has no finite-temperature phase transitions, we find that introducing a finite defect density n_{d}≈10^{-4}-10^{-2} produces a true phase transition with a sizeable T_{c}≈2n_{d} in units of the Kitaev exchange. The resulting non-Abelian chiral quantum spin liquid exhibits scalar spin chirality and electron orbital magnetization which peak near lattice defects. This disorder-driven instability relies on an emergent long range ferromagnetic interaction r^{-γ} (γ≈2.7) between defect chiralities, mediated by the nearly gapless fermions, with implications for topology generation in Dirac cones with fluctuating mass terms.
In this work we extend our study of the effect of certain crystallographic defects on the spin-1/2 Kitaev honeycomb spin liquid (arXiv:2511.19409), focusing on its gapless phase and contrasting with the gapped phase. We identify a Stone-Wales (SW) local defect consisting of a 90
∘ bond rotation that preserves Kitaev bond labels for edge-sharing octahedra and thereby enables exact solvability. These SW-type defects involve odd-sided plaquettes with
±π/2 fluxes, but can be created locally. An isolated defect hosts a time-reversal pair of ground-state flux configurations with large net chirality. Certain excitations are also chiral. The chirality manifests in Majorana local Chern marker and in scalar spin chirality, producing electronic orbital magnetization. T-matrix analysis and numerics at finite defect density
nd show that defect chiralities generate a topological gap of
11nd protecting a Chern number
C=±1. Emergent ferromagnetic long range Ising interactions
r−γ with
2<γ<3 between defect chiralities lead to a finite temperature
Tc phase transition into the chiral spin liquid. The
Tc is proportional to
nd and diverges when
γ→2. We also consider additional solvable impurity potentials and find that
γ can be reduced to below
2.3 and correspondingly enhance
Tc. Our results offer applications to 2D Dirac cone systems with a finite density of fluctuating Ising magnetic impurities and to identifying spin liquids with lattice defects.
We examine the star lattice Kitaev model whose ground state is a chiral spin liquid. We fermionize the model such that the fermionic vacua are toric-code states on an effective Kagome lattice. This implies that the Abelian phase of the system is inherited from the fermionic vacua and that time-reversal symmetry is spontaneously broken at the level of the vacuum. In terms of these fermions we derive the Bloch-matrix Hamiltonians for the vortex-free sector and its time-reversed counterpart and illuminate the relationships between the sectors. The phase diagram for the model is shown to be a sphere in the space of coupling parameters around the triangles of the lattices. The Abelian phase lies inside the sphere and the critical boundary between topologically distinct Abelian and non-Abelian phases lies on the surface. Outside the sphere the system is generically gapped except in the planes where the coupling parameters between the vertices on triangles are zero. These cases correspond to bipartite lattice structures and the dispersion relations are similar to that of the original Kitaev honeycomb model. In a further analysis we demonstrate the threefold non-Abelian ground-state degeneracy on a torus by explicit calculation.
We study a model in (2 + 1)-dimensional space-time that is realized by an array of chains, each of which realizes relativistic Majorana fields in (1 + 1)-dimensional space-time, coupled via current-current interactions. The model is shown to have a lattice realization as an array of coupled quantum spin-1/2 ladders. We study this model both in the presence and in the absence of time-reversal symmetry within a mean-field approximation. We find regimes in coupling space where Abelian and non-Abelian spin-liquid phases are stable. In the case when the Hamiltonian is time-reversal symmetric, we find regimes where gapped Abelian and non-Abelian chiral phases appear as a result of spontaneous breaking of time-reversal symmetry. These gapped phases are separated by a discontinuous phase transition. More interestingly, we find a regime for which a nonchiral gapless non-Abelian spin liquid is stable. The excitations in this regime are described by relativistic Majorana fields in (2 + 1)-dimensional space-time, much as those appearing in the Kitaev honeycomb model but here emerging in a model of coupled spin ladders that do not break the
SU(2) spin-rotation symmetry.