Coherent hole propagation in an exactly solvable gapless spin liquid

We examine the dynamics of a single hole in the gapless phase of the Kitaev honeycomb model, focusing on the slow-hole regime where the bare hopping amplitude $t$ is much less than the Kitaev exchange energy $J$. In this regime, the hole does not generate gapped flux excitations and is dressed only by the gapless fermion excitations. Investigating the single-hole spectral function, we find that the hole propagates coherently with a quasiparticle weight that is finite but approaches zero as $t/J\to 0$. This conclusion follows from two approximate treatments, which capture the same physics in complementary ways. Both treatments use the stationary limit as an exactly solvable starting point to study the spectral function approximately (i) by employing a variational approach in terms of a trial state that interpolates between the limits of a stationary hole and an infinitely fast hole and (ii) by considering a special point in the gapless phase that corresponds to a simplified one-dimensional problem.

Figure 1

Illustration of the honeycomb lattice. Sites in sublattices $A$ and $B$ are marked by white and black circles, while $x, y$, and $z$ bonds are marked by dotted, dashed, and solid lines, respectively.

Figure 2

Fermion coupling strengths around the instantaneous hole site (dotted circle) for the quadratic variational Hamiltonian ${\widehat{H}}_c\left(\varrho \right)$ at $t=0$ (left), finite $t$ (middle), and $t\to \infty$ (right). Default couplings $J_0$ are marked by solid lines, partially switched-off couplings $\varrho J_0$ are marked by dashed lines (where $0<\varrho <1$), and fully switched-off couplings 0 are marked by dotted lines.

Figure 3

Illustration of the one-dimensional (1D) chain with the lattice constant $\delta \mathbf{R}$ and the site labeling convention around the instantaneous hole site $\ell =0$ (dotted circle).

Figure 4

Quasiparticle weight $Z$ as a function of the system size $N$ for $t_K=0$ (a) and for $t_K\to \infty$ (b). Numerical data points are marked by black crosses, while asymptotic fits of the form $Z\propto N^{-0.125}$ (a) and $Z\approx 0.9716$ (b) are marked by red lines.