Single-hole spectra of Kitaev spin liquids: from dynamical Nagaoka ferromagnetism to spin-hole fractionalization

TL;DR

This paper investigates how a single hole affects the dynamical response of Kitaev spin liquids, revealing different behaviors in ferromagnetic and antiferromagnetic cases, and highlighting the potential of spectral functions to probe fractionalization.

Contribution

It provides the first tensor network simulation of a doped hole in Kitaev spin liquids, uncovering Nagaoka ferromagnetism and fractionalized holon-spinon spectra.

Findings

Nagaoka ferromagnetism forms around holes in ferromagnetic Kitaev liquids.

Hole spectra in antiferromagnetic cases show fractionalization into holons and spinons.

Numerical results agree with analytical models for slow holes.

Abstract

The dynamical response of a quantum spin liquid upon injecting a hole is a pertinent open question. In experiments, the hole spectral function, measured momentum-resolved in angle-resolved photoemission spectroscopy (ARPES) or locally in scanning tunneling microscopy (STM), can be used to identify spin liquid materials. In this study, we employ tensor network methods to simulate the time evolution of a single hole doped into the Kitaev spin-liquid ground state. Focusing on the gapped spin liquid phase, we reveal two fundamentally different scenarios. For ferromagnetic spin couplings, the spin liquid is highly susceptible to hole doping: a Nagaoka ferromagnet forms dynamically around the doped hole, even at weak coupling. By contrast, in the case of antiferromagnetic spin couplings, the hole spectrum demonstrates an intricate interplay between charge, spin, and flux degrees of freedom, best described by a parton mean-field ansatz of fractionalized holons and spinons. Moreover, we find a good agreement of our numerical results to the analytically solvable case of slow holes. Our results demonstrate that dynamical hole spectral functions provide rich information on the structure of fractionalized quantum spin liquids.