A vison is an excitation of the Kitaev spin liquid which carries a $mathbb Z_2$ gauge flux. While immobile in the pure Kitaev model, it becomes a dynamical degree of freedom in the presence of perturbations. We study an isolated vison in the isotropi
c Kitaev model perturbed by a small external magnetic field $h$, an offdiagonal exchange interactions $Gamma$ and a Heisenberg coupling $J$. In the ferromagnetic Kitaev model, the dressed vison obtains a dispersion linear in $Gamma$ and $h$ and a fully universal low-$T$ mobility, $mu=6 v_m^2/T^{2}$, where $v_m$ is the velocity of Majorana fermions. In contrast, in the antiferromagnetic Kitaev model interference effects preclude coherent propagation and an incoherent Majorana-assisted hopping leads to a $T$-independent mobility. The motion of a single vison due to Heisenberg interactions is strongly suppressed for both signs of the Kitaev coupling. Vison bands induced by $h$ are topological and lead to a characteristic peak in the thermal Hall effect as observed experimentally in $alpha$-RuCl$_3$.
In chiral magnets a magnetic helix forms where the magnetization winds around a propagation vector $mathbf{q}$. We show theoretically that a magnetic field $mathbf{B}_{perp}(t) perp mathbf{q}$, which is spatially homogeneous but oscillating in time,
induces a net rotation of the texture around $mathbf{q}$. This rotation is reminiscent of the motion of an Archimedean screw and is equivalent to a translation with velocity $v_{text{screw}}$ parallel to $mathbf{q}$. Due to the coupling to a Goldstone mode, this non-linear effect arises for arbitrarily weak $mathbf{B}_{perp}(t) $ with $v_{text{screw}} propto |mathbf{B}_{perp}|^2$ as long as pinning by disorder is absent. The effect is resonantly enhanced when internal modes of the helix are excited and the sign of $v_{text{screw}}$ can be controlled either by changing the frequency or the polarization of $mathbf{B}_{perp}(t)$. The Archimedean screw can be used to transport spin and charge and thus the screwing motion is predicted to induce a voltage parallel to $mathbf{q}$. Using a combination of numerics and Floquet spin wave theory, we show that the helix becomes unstable upon increasing $mathbf{B}_{perp}$ forming a `time quasicrystal which oscillates in space and time for moderately strong drive.
A typical strategy of realizing an adiabatic change of a many-particle system is to vary parameters very slowly on a time scale $t_text{r}$ much larger than intrinsic equilibration time scales. In the ideal case of adiabatic state preparation, $t_tex
t{r} to infty$, the entropy production vanishes. In systems with conservation laws, the approach to the adiabatic limit is hampered by hydrodynamic long-time tails, arising from the algebraically slow relaxation of hydrodynamic fluctuations. We argue that the entropy production $Delta S$ of a diffusive system at finite temperature in one or two dimensions is governed by hydrodynamic modes resulting in $Delta S sim 1/sqrt{t_text{r}}$ in $d=1$ and $Delta S sim ln(t_text{r})/t_text{r}$ in $d=2$. In higher dimensions, entropy production is instead dominated by other high-energy modes with $Delta S sim 1/t_text{r}$. In order to verify the analytic prediction, we simulate the non-equilibrium dynamics of a classical two-component gas with point-like particles in one spatial dimension and examine the total entropy production as a function of $t_text{r}$.
Weakly pumped systems with approximate conservation laws can be efficiently described by a generalized Gibbs ensemble if the steady state of the system is unique. However, such a description can fail if there are multiple steady state solutions, for
example, a bistability. In this case domains and domain walls may form. In one-dimensional (1D) systems any type of noise (thermal or non-thermal) will in general lead to a proliferation of such domains. We study this physics in a 1D spin chain with two approximate conservation laws, energy and the $z$-component of the total magnetization. A bistability in the magnetization is induced by the coupling to suitably chosen Lindblad operators. We analyze the theory for a weak coupling strength $epsilon$ to the non-equilibrium bath. In this limit, we argue that one can use hydrodynamic approximations which describe the system locally in terms of space- and time-dependent Lagrange parameters. Here noise terms enforce the creation of domains, where the typical width of a domain wall goes as $sim 1/sqrt{epsilon}$ while the density of domain walls is exponentially small in $1/sqrt{epsilon}$. This is shown by numerical simulations of a simplified hydrodynamic equation in the presence of noise.
Geometrically frustrated quantum impurities coupled to metallic leads have been shown to exhibit rich behavior with a quantum phase transition separating Kondo screened and local moment phases. Frustration in the quantum impurity can alternatively be
introduced via Kitaev-couplings between different spins of the impurity cluster. We use the Numerical Renormalization Group (NRG) to study a range of systems where the quantum impurity comprising a Kitaev cluster is coupled to a bath of non-interacting fermions. The models exhibits a competition between Kitaev and Kondo dominated physics depending on whether the Kitaev couplings are greater or less than the Kondo temperature. We characterize the ground state properties of the system and determine the temperature dependence of the crossover scale for the emergence of fractionalized degrees of freedom in the model. We also demonstrate qualitatively as well as quantitatively that in the Kondo limit, the complex impurity can be mapped to an effective two-impurity system, where the emergent spin $1/2$ comprises of both Majorana and flux degrees of freedom. For a tetrahedral-shaped Kitaev cluster, an extra orbital degree of freedom closely related to a flux degree of freedom remains unscreened even in the presence of both Heisenberg and Kondo interactions.
The recent observation of a half-integer quantized thermal Hall effect in $alpha$-RuCl$_3$ is interpreted as a unique signature of a chiral spin liquid with a Majorana edge mode. A similar quantized thermal Hall effect is expected in chiral topologic
al superconductors. The unavoidable presence of gapless acoustic phonons, however, implies that, in contrast to the quantized electrical conductivity, the thermal Hall conductivity $kappa_xy$ is never exactly quantized in real materials. Here, we investigate how phonons affect the quantization of the thermal conductivity focusing on the edge theory. As an example we consider a Kitaev spin liquid gapped by an external magnetic field coupled to acoustic phonons. The coupling to phonons destroys the ballistic thermal transport of the edge mode completely, as energy can leak into the bulk, thus drastically modifying the edge-picture of the thermal Hall effect. Nevertheless, the thermal Hall conductivity remains approximately quantized and we argue, that the coupling to phonons to the edge mode is a necessary condition for the observation of the quantized thermal Hall effect. The strength of this edge coupling does, however, not affect the conductivity. We argue that for sufficiently clean systems the leading correction to the quantized thermal Hall effect, $Delta kappa_{xy}/T sim text{sign(B)} , T^2$, arises from a intrinsic anomalous Hall effect of the acoustic phonons due to Berry phases imprinted by the chiral (spin) liquid in the bulk. This correction depends on the sign but not the amplitude of the external magnetic field.
