Coherent hole propagation in an exactly solvable gapless spin liquid

TL;DR

This paper studies the movement of a single hole in a gapless spin liquid described by the Kitaev honeycomb model, revealing coherent propagation with a quasiparticle weight that diminishes as hopping becomes very slow.

Contribution

It introduces two approximate methods to analyze hole dynamics in the gapless phase, providing insights into quasiparticle behavior in this exactly solvable model.

Findings

Hole propagates coherently with finite quasiparticle weight

Quasiparticle weight approaches zero as hopping amplitude decreases

Methods capture the same physics through different approximations

Abstract

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.