In the field of quantum magnetism, the exactly solvable Kitaev honeycomb model serves as a paradigm for the fractionalization of spin degrees of freedom and the formation of [Formula: see text] quantum spin liquids. An intense experimental search has led to the discovery of a number of spin-orbit entangled Mott insulators that realize its characteristic bond-directional interactions and, in the presence of magnetic fields, exhibit no indications of long-range order. Here, we map out the complete phase diagram of the Kitaev model in tilted magnetic fields and report the emergence of a distinct gapless quantum spin liquid at intermediate field strengths. Analyzing a number of static, dynamical, and finite temperature quantities using numerical exact diagonalization techniques, we find strong evidence that this phase exhibits gapless fermions coupled to a massless U(1) gauge field. We discuss its stability in the presence of perturbations that naturally arise in spin-orbit entangled candidate materials.
The ruby lattice is a four-valent lattice interpolating between honeycomb and triangular lattices. In this work we investigate the topological spin-liquid phases of a spin Hamiltonian with Kitaev interactions on the ruby lattice using exact diagonalization and perturbative methods. The latter interactions combined with the structure of the lattice yield a model with ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ gauge symmetry. We mapped out the phase diagram of the model and found gapped and gapless spin-liquid phases. While the low-energy sector of the gapped phase corresponds to the well-known topological color code model on a honeycomb lattice, the low-energy sector of the gapless phases is described by an effective spin model with three-body interactions on a triangular lattice. A gap is opened in the spectrum in small magnetic fields, where we showed that the ground state has a finite topological entanglement entropy. We argue that the gapped phases could be possibly described by exotic excitations, and their corresponding spectrum is richer than the Ising phase of the Kitaev model.
The Kitaev honeycomb model supports gapless and gapped quantum spin liquid phases. Its exact solvability relies on extensively many locally conserved quantities. Any real-world manifestation of these phases would include imperfections in the form of disorder and interactions that break integrability. We show that the latter qualitatively alters the properties of vacancies in the gapless Kitaev spin liquid: (i) Isolated vacancies carry a magnetic moment, which is absent in the exactly solvable case. (ii) Pairs of vacancies on even or opposite sublattices gap each other with distinct power laws that reveal the presence of emergent gauge flux.
The quest for Kitaev quantum spin liquids has led to great interest in honeycomb quantum magnets with strong spin-orbit coupling. It has been recently proposed that even Mott insulators with
3d transition metal ions, having nominally weak spin-orbit coupling, can realize such exotic physics. Motivated by this, we study the rhombohedral honeycomb cobaltates CoTiO
3, BaCo
2(PO
4)
2, and BaCo
2(AsO
4)
2, using
ab initio density functional theory, which takes into account realistic crystal field distortions and chemical information, in conjunction with exact diagonalization numerics. We show that these Co
2+ magnets host
jeff=1/2 local moments with highly anisotropic
g-factors, and we extract their full spin Hamiltonians including longer-range and anisotropic exchange couplings. For CoTiO
3, we find a nearest-neighbor easy-plane ferromagnetic
XXZ model with additional bond-dependent anisotropies and interlayer exchange, which supports three-dimensional (3D) Dirac nodal line magnons. In contrast, for BaCo
2(PO
4)
2 and BaCo
2(AsO
4)
2, we find a strongly suppressed interlayer coupling, and significant frustration from additional third-neighbor antiferromagnetic exchange mediated by P/As. Such bond-anisotropic
J1-
J3 spin models can support collinear zig-zag or coplanar spiral ground states; we discuss their dynamical spin correlations which reveal a gapped Goldstone mode, and argue that the effective parameters of these pseudospin-
1/2 models may be strongly renormalized by coupling to a low energy spin-exciton. Our results call for re-examining proposals for realizing Kitaev spin liquids in the honeycomb cobaltates.
The exactly solvable spin-1/2 Kitaev model on a honeycomb lattice has drawn significant interest, as it offers a pathway to realizing the long-sought-after quantum spin liquid. Building upon the Kitaev model, Yao and Lee introduced another exactly solvable model on an unusual star lattice featuring non-abelian spinons. The additional pseudospin degrees of freedom in this model could provide greater stability against perturbations, making this model appealing. However, a mechanism to realize such an interaction in a standard honeycomb lattice remains unknown. Here, we provide a microscopic theory to obtain the Yao-Lee model, on a honeycomb lattice by utilizing strong spin-orbit coupling of anions edge-shared between two e g ions in the exchange processes. This mechanism leads to the desired bond-dependent interaction among spins rather than orbitals, unique to our model, implying that the orbitals fractionalize into gapless Majorana fermions and fermionic octupolar excitations emerge. Since the conventional Kugel-Khomskii interaction also appears, we examine the phase diagram, including these interactions, using classical Monte Carlo simulations and exact diagonalization techniques. Our findings reveal a broad region of disordered states that break rotational symmetry in the bond energy, suggesting intriguing behavior reminiscent of a spin-orbital liquid.
The formation of quantum spin liquids in frustrated magnets represents an exciting possibility due to the rather exotic features they harbor, including fractionalized excitations and emergent gauge fields. \nUnfortunately, they are notoriously difficult to study as there are often no good analytical methods available and quantum Monte Carlo simulations are hindered by the negative sign problem. \nThe Kitaev honeycomb model is a notable exception of a frustrated quantum model which is exactly solvable and which hosts a number of distinct quantum spin liquid ground states. \nAs such, it allows for a rare opportunity to study the physics of spin liquids with full analytical control. \n \nIn this thesis, we study the fractionalization of spin-1/2 moments into Majorana fermions and an emergent Z2 gauge field in a generalization of the Kitaev honeycomb model to a number of three-dimensional lattices. \nWhile the excitations of the gauge field are always gapped, the fermionic quasiparticles may exhibit a gapless dispersion, forming fully two-dimensional Fermi surfaces, symmetry protected nodal lines, or topological Weyl nodes. \nWe show that one can deduce rather general constraints on the possible gapless excitations by making use of an object called the projective symmetry group. \nIn doing so we provide a scheme for classifying the various gapless Kitaev spin liquids. \nA thorough analysis is carried out for a number of these spin liquids, primarily investigating the stability of the gapless modes and the novel features resulting from their sometimes non-trivial topology, as well as their effects on certain equal-time correlation functions.