Three-dimensional Kitaev models -- generalizations of the well known exactly solvable Kitaev honeycomb model -- exhibit a rich variety of quantum spin liquid phases. Their fractionalized excitations are Majorana fermions that may form topological band structures. These can be enriched by lattice symmetries, as shown in the present work. In particular, the authors propose two new instances of Kitaev spin liquids that exhibit nodal chains and 3D Dirac nodes in the bulk. Such crystalline Kitaev spin liquids are direct generalizations of crystalline topological insulators, albeit in an interacting spin system. A potential material realization in metal-organic frameworks is also discussed.
The recently introduced topological quantum chemistry (TQC) framework has provided a description of universal topological properties of all possible band insulators in all space groups based on crystalline unitary symmetries and time reversal. While this formalism filled the gap between the mathematical classification and the practical diagnosis of topological materials, an obvious limitation is that it only applies to weakly interacting systems, which can be described within band theory. It is an open question to which extent this formalism can be generalized to correlated systems that can exhibit symmetry-protected topological phases which are not adiabatically connected to any band insulator. In this work, we address the many facets of this question by considering the specific example of an extended version of a Hubbard diamond chain. This model features a Mott insulator, a trivial insulating phase, and an obstructed atomic limit phase. Here we first discuss the nature of the Mott insulator and determine the phase diagram and topology of the interacting model with infinite density matrix renormalization group calculations, variational Monte Carlo simulations, and with many-body topological invariants. We then proceed by considering a generalization of the TQC formalism to Green's functions combined with the concept of a topological Hamiltonian to identify the topological nature of the phases. Here we use cluster perturbation theory to calculate the Green's functions. The results are benchmarked with the above-determined phase diagram, and we discuss the applicability and limitations of the approach and its possible extensions in the diagnosis of topological phases in materials, in contrast to the use of many-body topological invariants.
Quantum spin liquids have fascinated condensed matter physicists for decades because of their unusual properties such as spin fractionalization and long-range entanglement. Unlike conventional symmetry breaking, the topological order underlying quantum spin liquids is hard to detect experimentally. Even theoretical models are scarce for which the ground state is established to be a quantum spin liquid. The Kitaev honeycomb model and its generalizations to other tricoordinated lattices are chief counterexamples—they are exactly solvable, harbor a variety of quantum spin liquid phases, and are also relevant for certain transition metal compounds including the polymorphs of (Na,Li) 2 IrO 3 iridates and RuCl 3 . In this review, we give an overview of the rich physics of the Kitaev model, including two-dimensional and three-dimensional fractionalization as well as dynamic correlations and behavior at finite temperatures. We discuss the different materials and argue how the Kitaev model physics can be relevant even though most materials show magnetic ordering at low temperatures.
The Kitaev honeycomb model has attracted significant interest due to its quantum spin liquid ground state, fractionalized Majorana excitations, and topological properties. Motivated by these features, we introduce a quasi-one-dimensional Kitaev-like spin chain derived from a truncated honeycomb geometry. The resulting Majorana band structure contains both dispersive and flat bands, with a gap closing at a critical anisotropy that separates trivial and chiral topological phases. Under open boundary conditions, the topological regime hosts zero-energy edge modes protected by chiral symmetry, placing the system in the BDI symmetry class with a quantized winding number. In the excited spectrum, localized plaquette modes emerge near zero energy and can be tuned by introducing domains of negative plaquettes. The dynamical spin correlation function reveals broad continua associated with fractionalized excitations, together with characteristic low-energy spectral weight from edge Majorana modes. These features distinguish the present system from conventional Heisenberg spin chains and provide experimentally relevant fingerprints of chiral topological order. Our model thus establishes a conceptual bridge between the two-dimensional Kitaev spin liquid and Kitaev's one-dimensional quantum wire.
A large part of modern condensed matter concerns non-local or global properties of systems under the broad term of topology. Closely intertwined with certain senses of topology are symmetries of the system, which physically constrain our description and offer non-perturbative insights into material properties. The range of possible phases of matter is greatly enriched by quantum mechanics, including certain types of non-local entanglement that cannot be understood in the usual symmetry-breaking paradigm of local order parameters. Beyond weakly interacting topology we find the stronger notion of \textit{topological order} in correlated systems, a prominent example being the
S=21 Kitaev honeycomb model in a weak magnetic field.Through a remarkable combination of lattice geometry, strong spin-orbit coupling, and electron interactions, several material candidates have been put forward to realize Kitaev physics, including the
4d Mott insulator
α-RuCl
3 which offers tantalizing experimental hints of topological order. In this thesis we explore several aspects of Kitaev candidates and related systems under two broad themes. One involves symmetry-informed and constrained observables, including a proposed singularity in a thermodynamic quantity accompanying phase transitions between two Ising topological orders (ITOs). The ITO physics realized by the Kitaev model requires time-reversal symmetry to be broken, and much of the non-trivial physics is found at finite magnetic field. To this end, we study a microscopic spin model appropriate for
α-RuCl
3 and show that it exhibits an interesting field-induced paramagnetic state between the low- and high-field magnetic orders, consistent with recent experimental findings. We determine several properties of a lower-dimensional spin-
S analogue of the Kitaev model, including a multi-critical point at finite field separating different topological phases. Finally, we derive quantum state purities of entangled photons emitted from a spin-triplet superconducting heterostructure and discuss its use in a new paradigm of entangled spectroscopy.
Topological aspects, widely discussed in relation to fermionic systems, need not be restricted to the ground state of electrons. The excitation spectrum in certain frustrated quantum magnets could be topological in nature. The Kitaev-Heisenberg model is a cornerstone in the study of quantum spin-liquid candidate materials such as Na
2IrO
3 and RuCl
3. Here, the author presents the interesting and surprising result that the quasiparticles in the ferromagnetic Kitaev-Heisenberg model have a nontrivial Berry curvature leading to a nonzero Chern-number topological invariant. Consequently, there are chiral edge excitations along the zigzag edge, which can be detected in scattering and in thermal- or spin-transport experiments.