ABSTRACT
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.
ABSTRACT
The S=3/2 Kitaev honeycomb model (KHM) is a quantum spin liquid (QSL) state coupled to a static Z2 gauge field. Employing an SO(6) Majorana representation of spin3/2's, we find an exact representation of the conserved plaquette fluxes in terms of static Z2 gauge fields akin to the S=1/2 KHM which enables us to treat the remaining interacting matter fermion sector in a parton mean-field theory. We uncover a ground-state phase diagram consisting of gapped and gapless QSLs. Our parton description is in quantitative agreement with numerical simulations, and is furthermore corroborated by the addition of a [001] single ion anisotropy (SIA) which continuously connects the gapless Dirac QSL of our model with that of the S=1/2 KHM. In the presence of a weak [111] SIA, we discuss an emergent chiral QSL within a perturbation theory.
ABSTRACT
Strongly correlated materials with strong spin-orbit coupling hold promise for realizing topological phases with fractionalized excitations. Here, we propose a chiral spin-orbital liquid as a stable phase of a realistic model for heavy-element double perovskites. This spin liquid state has Majorana fermion excitations with a gapless spectrum characterized by nodal lines along the edges of the Brillouin zone. We show that the nodal lines are topological defects of a non-Abelian Berry connection and that the system exhibits dispersing surface states. We discuss some experimental signatures of this state and compare them with properties of the spin liquid candidate Ba_{2}YMoO_{6}.
