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arXiv:2309.15157 · npj Quantum Materials

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

Wilhelm Kadow, Hui-Ke Jin, Johannes Knolle, Michael Knap

Published Mar 21, 2024• 8 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/s41535-024-00641-7

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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.
The complex interplay between charge and spin dynamics lies at the heart of strongly correlated quantum materials, and it is a fundamental topic in basic research with far-reaching technological perspectives. We explore in this paper the dynamics of holes in a single-band, extended t - J model where the background spins form a Z 2 quantum spin liquid. Using a field theory approach based on a parton construction, we show that while the electrons for most momenta fractionalize into uncorrelated charge-carrying holons and spin-carrying spinons as generally expected for a quantum spin liquid, the spinon-holon scattering cross section diverges for certain momenta, signaling strong correlations. By deriving an effective low-energy Hamiltonian describing this dynamics, we demonstrate that these divergences are due to the formation of long-lived spinon-holon bound states. Since the wave function of these bound states is localized over a few lattice sites, they correspond to well-defined fermions with the same charge and spin as the underlying electrons. We then show that quantum gas microscopy with atoms in optical lattices provides an excellent platform for verifying and probing the internal spatial structure of these emerging fermions. The fermions will furthermore show up as clear quasiparticle peaks in angle-resolved photoemission spectroscopy with an intensity determined by their internal structure. For a nonzero hole concentration, the fermions form hole pockets with qualitatively the same location, shape, and intensity variation in the Brillouin zone as the so-called Fermi arcs observed in the pseudogap phase. Such agreement is remarkable since the Fermi arcs arise from the delicate interplay between the symmetry of the quantum spin liquid and the internal structure of the emerging fermions in a minimal single-band model with no extra degrees of freedom added. Our results, therefore, provide a microscopic mechanism for the conjectured fractionalized Fermi liquid and open up new pathways for exploring the pseudogap phase and high-temperature superconductivity as arising from a quantum spin liquid.
Abstract We study the effect of hole doping on the Kitaev spin liquid (KSL) and find that for ferromagnetic (FM) Kitaev exchange K the system is very susceptible to the formation of a FM spin polarization. Through density matrix renormalization group (DMRG) simulations on finite systems, we uncover that the introduction of a single hole with a hopping strength of just t~0.28K is enough to disrupt fractionalization and polarize the spins in the [001] direction due to an order-by-disorder mechanism. Taking into account a material relevant FM anisotropic spin exchange KΓK drives the polarization towards the [111] direction via a reorientation transition into a topological FM state with chiral magnon excitations. We develop a parton mean-field theory incorporating fermionic holons and bosonic spinons/magnons, which accounts for the doping induced FM phases and topological magnon excitations. We discuss experimental signatures and implications for Kitaev candidate materials.
We explore with exact diagonalization the propagation of a single hole in four magnetic phases of the $t\text{\ensuremath{-}}J$-like Kitaev-Heisenberg model on a honeycomb lattice: the N\'eel antiferromagnetic, stripe, zigzag, and Kitaev spin-liquid phases. We find coherent propagation of spin-polaron quasiparticles in the antiferromagnetic phase by a mechanism similar to that in the $t\text{\ensuremath{-}}J$ model for high-Tc{T}_{c}Tc​ cuprates. In the stripe and zigzag phases clear quasiparticles features appear in spectral functions of those propagators where holes are created and annihilated on one sublattice, while they remain largely hidden in those spectral functions that correspond to photoemission experiments. As the most surprising result, we find a totally incoherent spectral weight distribution for the spectral function of a hole moving in the Kitaev spin-liquid phase in the strong-coupling regime $t\ensuremath{\gg}J$ relevant for iridates. At intermediate coupling the finite systems calculation reveals a well-defined quasiparticle at the $\ensuremath{\Gamma}$ point; however, we find that the gapless spin excitations wipe out quasiparticles at finite momenta. Also for this more subtle case we conclude that in the thermodynamic limit the lightly doped Kitaev liquid phase does not support quasiparticle states in the neighborhood of $\ensuremath{\Gamma}$, and therefore yields a non-Fermi liquid, contrary to earlier suggestions based on slave-boson studies. These observations are supported by the presented study of the dynamic spin-structure factor in the Kitaev spin liquid regime.
We present a controlled microscopic study of mobile holes in the spatially anisotropic (Abelian) gapped phase of the Kitaev honeycomb model. We address the properties of (i) a single hole (its internal degrees of freedom as well as its hopping properties); (ii) a pair of holes [their (relative) particle statistics and interactions]; and (iii) the collective state for a finite density of holes. We find that each hole in the doped model has an eight-dimensional internal space, characterized by three internal quantum numbers: the first two ``fractional'' quantum numbers describe the binding to the hole of the fractional excitations (fluxes and fermions) of the undoped model, while the third ``spin'' quantum number determines the local magnetization around the hole. The fractional quantum numbers also encode fundamentally distinct particle properties, topologically robust against small local perturbations: some holes are free to hop in two dimensions, while others are confined to hop in one dimension only; distinct hole types have different particle statistics, and in particular, some of them exhibit nontrivial (anyonic) relative statistics. These particle properties in turn determine the physical properties of the multihole ground state at finite doping, and we identify two distinct ground states with different hole types that are stable for different model parameters. The respective hopping dimensionalities manifest themselves in an electrical conductivity approximately isotropic in one ground state and extremely anisotropic in the other one. We also compare our microscopic study with related mean-field treatments, and discuss the main discrepancies between the two approaches, which in particular involve the possibility of binding fractional excitations as well as the particle statistics of the holes. On a technical level, we describe the hopping of mobile holes via a quasistationary approach, where effective hopping matrix elements are calculated between ground states with stationary holes at different positions. This approach relies on the fact that the model remains exactly solvable in the presence of stationary holes, and that the motion of sufficiently slow holes does not generate bulk excitations in a gapped phase. When the bare hopping amplitude is much smaller than the energy gap, many of our results, in particular those on the hopping properties and the particle statistics, are exact.
We study the dynamics of fractionalized excitations in a Kitaev spin liquid (KSL) induced by a local magnetic field perpendicular to the Kitaev honeycomb lattice. The local magnetic field induces a dynamic excitation of a pair of fluxes described by a generally particle-hole asymmetric interacting resonant level model and the dynamics resembles that of a Kondo problem. The p-h asymmetry competes with the magnetic field and results in a rich phase diagram. Moreover, the magnetic field breaks the gauge equivalence of the ferromagnetic (FM) and anti-ferromagnetic (AFM) Kitaev couplings of the ground state and leads to dramatically different behaviors for the two cases. The latter experiences a first order phase transition during magnetization whereas the former does not. By studying the response of the KSL to the magnetic field in different regimes, we obtain the RG flow and phase diagram of the system in the whole space. This study can be generalized to the KSL in a uniform magnetic field and help resolve issues in recent experiments on KSL candidates.
We study the response of a Kitaev spin liquid (KSL) to a local magnetic field perpendicular to the Kitaev honeycomb lattice. The local magnetic field induces a dynamical excitation of a flux pair in the spin liquid and the system can be described by a generally particle-hole asymmetric interacting resonant level model. The dynamical excitation of the flux pair closes the flux gap in the spectrum of the spin correlation function locally for the gapless KSL even from the perturbative response to a weak magnetic field. Beyond the perturbative regime, the p-h asymmetry competes with the magnetic field and results in a rich phase diagram. Moreover, the magnetic field breaks the gauge equivalence of the ferromagnetic and antiferromagnetic Kitaev couplings of the ground state and leads to very different behaviors for the two cases. The antiferromagnetic case experiences a first-order phase transition to the polarized state during magnetization, whereas the ferromagnetic case does not. This study can be generalized to the Kitaev model in a uniform magnetic field and may help understand issues in recent experiments on KSL candidates.