Motivated by recent experiments on α-RuCl3, we investigate a possible quantum spin liquid ground state of the honeycomb-lattice spin model with bond-dependent interactions. We consider the K − Γ model, where K and Γ represent the Kitaev and symmetric-anisotropic interactions between spin-1/2 moments on the honeycomb lattice. Using the infinite density matrix renormalization group (iDMRG), we provide compelling evidence for the existence of quantum spin liquid phases in an extended region of the phase diagram. In particular, we use transfer matrix spectra to show the evolution of two-particle excitations with well-defined two-dimensional dispersion, which is a strong signature of quantum spin liquid. These results are compared with predictions from Majorana mean-field theory and used to infer the quasiparticle excitation spectra. Further, we compute the dynamical structure factor using finite size cluster computations and show that the results resemble the scattering continuum seen in neutron scattering experiments on α-RuCl3. We discuss these results in light of recent and future experiments.

We investigate the superfluid properties of two-dimensional driven Bose liquids, such as polariton condensates, using their long-wavelength description in terms of a compact Kardar-Parisi-Zhang (KPZ) equation for the phase dynamics. We account for topological defects (vortices) in the phase field through a duality mapping between the compact KPZ equation and a theory of non-linear electrodynamics coupled to charges. Using the dual theory we derive renormalization group equations that describe vortex unbinding in these media. When the non-equilibirum drive is turned off, the KPZ non-linearity λ vanishes and the RG flow gives the usual Kosterlitz-Thouless (KT) transition. On the other hand, with non-linearity λ > 0 vortices always unbind, even if the same system with λ = 0 is superfluid. We predict the finite size scaling behavior of the superfluid stiffness in the crossover governed by vortex unbinding showing its clear distinction from the scaling associated with the KT transition. arXiv:1604.01042v3 [cond-mat.quant-gas]

The spin liquid phase is one of the prominent strongly interacting topological phases of matter whose unambiguous confirmation is yet to be reached despite intensive experimental efforts on numerous candidate materials. Recently, a new family of correlated honeycomb materials, in which strong spin-orbit coupling allows for various bond-dependent spin interactions, have been promising candidates to realize the Kitaev spin liquid. Here we study a model with bond-dependent spin interactions and show numerical evidence for the existence of an extended quantum spin liquid region, which is possibly connected to the Kitaev spin liquid state. These results are used to provide an explanation of the scattering continuum seen in neutron scattering on α-RuCl 3 .

A comprehensive theory of the Kosterlitz-Thouless transition in two-dimensional superfluids in thermal equilibrium can be developed within a dual representation which maps vortices in the superfluid to charges in a Coulomb gas. In this framework, the dissociation of vortex-antivortex pairs at the critical temperature corresponds to the formation of a plasma of free charges. The physics of vortex unbinding in driven-dissipative systems such as fluids of light, on the other hand, is much less understood. Here we make a crucial step to fill this gap by deriving a transformation that maps the compact Kardar-Parisi-Zhang (KPZ) equation, which describes the dynamics of the phase of a driven-dissipative condensate, to a dual electrodynamic theory. The latter is formulated in terms of modified Maxwell equations for the electromagnetic fields and a diffusion equation for the charges representing vortices in the KPZ equation. This mapping utilizes an adaption of the Villain approximation to a generalized Martin-Siggia-Rose functional integral representation of the compact KPZ equation on a lattice.