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Register a new userCompetition between Kondo and Kitaev Physics in Kitaev clusters coupled to a fermionic bath
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Added by
Tathagata Chowdhury
Publication date
2019
fields
Physics
and research's language is
English
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Geometrically frustrated quantum impurities coupled to metallic leads have been shown to exhibit rich behavior with a quantum phase transition separating Kondo screened and local moment phases. Frustration in the quantum impurity can alternatively be introduced via Kitaev-couplings between different spins of the impurity cluster. We use the Numerical Renormalization Group (NRG) to study a range of systems where the quantum impurity comprising a Kitaev cluster is coupled to a bath of non-interacting fermions. The models exhibits a competition between Kitaev and Kondo dominated physics depending on whether the Kitaev couplings are greater or less than the Kondo temperature. We characterize the ground state properties of the system and determine the temperature dependence of the crossover scale for the emergence of fractionalized degrees of freedom in the model. We also demonstrate qualitatively as well as quantitatively that in the Kondo limit, the complex impurity can be mapped to an effective two-impurity system, where the emergent spin $1/2$ comprises of both Majorana and flux degrees of freedom. For a tetrahedral-shaped Kitaev cluster, an extra orbital degree of freedom closely related to a flux degree of freedom remains unscreened even in the presence of both Heisenberg and Kondo interactions.
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Anyonic excitations emerging from a Kitaev spin liquid can form a basis for quantum computers. Searching for such excitations motivated intense research on the honeycomb iridate materials. However, access to a spin liquid ground state has been hindered by magnetic ordering. Cu2IrO3 is a new honeycomb iridate without thermodynamic signatures of a long-range order. Here, we use muon spin relaxation to uncover the magnetic ground state of Cu2IrO3. We find a two-component depolarization with slow and fast relaxation rates corresponding to distinct regions with dynamic and static magnetism, respectively. X-ray absorption spectroscopy and first principles calculations identify a mixed copper valence as the origin of this behavior. Our results suggest that a minority of Cu2+ ions nucleate regions of static magnetism whereas the majority of Cu+/Ir4+ on the honeycomb lattice give rise to a Kitaev spin liquid.
Paramagnetic impurities in a quantum spin-liquid can result in Kondo effects with highly unusual properties. We have studied the effect of locally exchange-coupling a paramagnetic impurity with the spin-1/2 honeycomb Kitaev model in its gapless spin-liquid phase. The (impurity) scaling equations are found to be insensitive to the sign of the coupling. The weak and strong coupling fixed points are stable, with the latter corresponding to a noninteracting vacancy and an interacting, spin-1 defect for the antiferromagnetic and ferromagnetic cases respectively. The ground state in the strong coupling limit in both cases has a nontrivial topology associated with a finite Z2 flux at the impurity site. For the antiferromagnetic case, this result can be obtained straightforwardly owing to the integrability of the Kitaev model with a vacancy. The strong-coupling limit of the ferromagnetic case is however nonintegrable, and we address this problem through exact-diagonalization calculations with finite Kitaev fragments. Our exact diagonalization calculations indicate that that the weak to strong coupling transition and the topological phase transition occur rather close to each other and are possibly coincident. We also find an intriguing similarity between the magnetic response of the defect and the impurity susceptibility in the two-channel Kondo problem.
The cooperative behavior of quantum impurities on 2D materials, such as graphene and bilayer graphene, is characterized by a non-trivial competition between screening (Kondo effect), and Ruderman-Kittel-Kasuya-Yosida (RKKY) magnetism. In addition, due to the small density of states at the Fermi level, impurities may not couple to the conduction electrons at all, behaving as free moments. Employing a recently developed {em{exact}} numerical method to study multi-impurity lattice systems, we obtain non-perturbative results that dramatically depart from expectations based on the conventional RKKY theory. At half-filling and for weak coupling, impurities remain in the local moment regime when they are on opposite sublattices, up to a critical value of the interactions when they start coupling anti-ferromagnetically with correlations that decay very slowly with inter-impurity distance. At finite doping, away from half-filling, ferromagnetism is completely absent and the physics is dominated by a competition between anti-ferromagnetism and Kondo effect. In bilayer graphene, impurities on opposite layers behave as free moments, unless the interaction is of the order of the hopping or larger.
The Kitaev model is a beautiful example of frustrated interactions giving rise to deep and unexpected phenomena. In particular, its classical version has remarkable properties stemming from exponentially large ground state degeneracy. Here, we present a study of magnetic clusters with spin-$S$ moments coupled by Kitaev interactions. We focus on two cluster geometries -- the Kitaev square and the Kitaev tetrahedron -- that allow us to explicitly enumerate all classical ground states. In both cases, the classical ground state space (CGSS) is large and self-intersecting, with non-manifold character. The Kitaev square has a CGSS of four intersecting circles that can be embedded in four dimensions. The tetrahedron CGSS consists of eight spheres embedded in six dimensions. In the semi-classical large-$S$ limit, we argue for effective low energy descriptions in terms of a single particle moving on these non-manifold spaces. Remarkably, at low energies, the particle is tied down in bound states formed around singularities at self-intersection points. In the language of spins, the low energy physics is determined by a distinct set of states that lies well below other eigenstates. These correspond to `Cartesian states, a special class of classical ground states that are constructed from dimer covers of the underlying lattice. They completely determine the low energy physics despite being a small subset of the classical ground state space. This provides an example of order by singularity, where state selection becomes stronger upon approaching the classical limit.
Kitaev materials are promising materials for hosting quantum spin liquids and investigating the interplay of topological and symmetry-breaking phases. We use an unsupervised and interpretable machine-learning method, the tensorial-kernel support vector machine, to study the honeycomb Kitaev-$Gamma$ model in a magnetic field. Our machine learns the global classical phase diagram and the associated analytical order parameters, including several distinct spin liquids, two exotic $S_3$ magnets, and two modulated $S_3 times Z_3$ magnets. We find that the extension of Kitaev spin liquids and a field-induced suppression of magnetic order already occur in the large-$S$ limit, implying that critical parts of the physics of Kitaev materials can be understood at the classical level. Moreover, the two $S_3 times Z_3$ orders are induced by competition between Kitaev and $Gamma$ spin liquids and feature a different type of spin-lattice entangled modulation, which requires a matrix description instead of scalar phase factors. Our work provides a direct instance of a machine detecting new phases and paves the way towards the development of automated tools to explore unsolved problems in many-body physics.
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