We discuss one-dimensional(1D) spin compass model or 1D Kitaev model in the presence of local bond defects. Three types of local disorders concerning both bond-nature and bond-strength that occur on kitaev materials have been investigated. Using exact diagonalization, two-point spin-spin structural correlations and four-point Out-of-Time-Order Correlators(OTOC) have been computed for the defective spin chains. The proposed quantities give signatures of these defects in terms of their responses to location and strength of defects. A key observation is that the information in the OTOC space gets trapped at the defect site giving rise to the phenomena of localization of information thus making these correlators a suitable diagnostic tool to detect and characterize these defects.
We discuss one-dimensional(1D) spin compass model or 1D Kitaev model in the presence of local bond defects. Three types of local disorders concerning both bond-nature and bond-strength that occur on kitaev materials have been investigated. Using exact diagonalization, two-point spin-spin structural correlations and four-point Out-of-Time-Order Correlators(OTOC) have been computed for the defective spin chains. The proposed quantities give signatures of these defects in terms of their responses to location and strength of defects. A key observation is that the information in the OTOC space gets trapped at the defect site giving rise to the phenomena of localization of information thus making these correlators a suitable diagnostic tool to detect and characterize these defects.
Abstract We discuss one-dimensional(1D) spin compass model or 1D Kitaev model in the presence of local bond defects. Three types of local disorders concerning both bond-nature and bond-strength that occur on kitaev materials have been investigated. Using exact diagonalization, two-point spin-spin structural correlations and four-point Out-of-Time-Order Correlators(OTOC) have been computed for the defective spin chains. The proposed quantities give signatures of these defects in terms of their responses to location and strength of defects. A key observation is that the information scrambling in the OTOC space gets trapped at the defect site giving rise to the phenomena of localization of information scrambling thus making these correlators a suitable diagnostic tool to detect and characterize these defects.
Motivated by intense research on two-dimensional spin-21 Kitaev materials, Kitaev spin chains and ladders, though geometrically limited, have been studied for their numerical simplicity and insights into extended Kitaev models. The phase diagrams under the magnetic field were also explored for these quasi-one-dimensional models. For an isotropic Kitaev chain, it was found that a magnetic field polarizes the ground state except along the symmetric field angle, where the chain is found to remain gapless up to a critical field strength where it enters an intriguing soliton phase before reaching the polarized state at higher field strengths. Here we study an anisotropic Kitaev chain under a magnetic field using the density matrix renormalization group technique, where the ground state has a macroscopic degeneracy with a finite gap in the absence of the magnetic field. When the field is mainly aligned parallel to the strong bond, four-site and large unit-cell ordered phases arise. In a certain angle of the field, another ordered phase characterized by a uniform chirality with six-site periodicity emerges. We employ a perturbation theory to understand such field-induced ordered phases. The effective model uncovers the presence of transverse Ising and Dzyaloshinskii-Moriya interactions between unit cells, as well as further-neighbor Ising interaction induced by the magnetic field, which collectively explain the mechanisms behind these ordered states. Open questions and challenges are also discussed.
The inherent complexity of interacting quantum many-body systems poses an outstanding challenge to both theory and experiment. Especially in the presence of strong electronic correlations, highly interesting and perplexing physical phenomena can occur. \nIn this thesis, we focus on three different examples of strongly correlated electron systems in which different types of defects occur. First, we investigate the Heisenberg-Kitaev model formulated on a triangular lattice. Using a mixture of numerical and analytical techniques we map out the entire phase diagram for the classical and quantum models. We provide an analytical foundation to the intriguing Z2-vortex ground state, in which strong spin-orbit coupling leads to the formation of a lattice of topological point defects. This state was observed previously in classical Monte Carlo simulations. We furthermore propose the iridate Ba3IrTi2O9 to be a prime candidate for the realization of such a state. \nThe second part deals with the physics of a defect in the form of a localized magnetic moment which is embedded into a metallic environment: the Kondo effect. Although this effect has been a cornerstone of condensed matter physics for more than 50 years, its properties in real-space are still not fully understood. What is the Kondo screening cloud---the extended many-body state of entangled conduction electrons? We present numerical results in 1D and 2D for the charge density oscillations created by the impurity. We find that the entire RG flow of the problem is recovered in these oscillations, elucidating the internal structure of the screening cloud. \nFinally, we investigate the competition between the Kondo effect and Majorana physics. Majorana bound states are highly interesting objects which exhibit unusual statistics and could be used as a building block of a topological quantum computer. Recently, signatures of their existence were observed in experiment, and we here examine how Kondo physics (which might play a role in real systems) interact with such Majorana bound states.
The Kitaev model is a fascinating example of an exactly solvable model displaying a spin-liquid ground state in two dimensions. However, deviations from the original Kitaev model are expected to appear in real materials. In this Letter, we investigate the fate of Kitaev's spin liquid in the presence of disorder-bond defects or vacancies-for an extended version of the model. Considering static flux backgrounds, we observe a power-law divergence in the low-energy limit of the density of states with a nonuniversal exponent. We link this power-law distribution of energy scales to weakly coupled droplets inside the bulk, in an uncanny similarity to the Griffiths phase often present in the vicinity of disordered quantum phase transitions. If time-reversal symmetry is broken, we find that power-law singularities are tied to the destruction of the topological phase of the Kitaev model in the presence of bond disorder alone. However, there is a transition from this topologically trivial phase with power-law singularities to a topologically nontrivial one for weak to moderate site dilution. Therefore, diluted Kitaev materials are potential candidates to host Kitaev's chiral spin-liquid phase.
Paramagnetic impurities in a quantum spin liquid give rise to Kondo effects with highly unusual properties. We have studied the effect of locally coupling a paramagnetic impurity with the spin-21 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 has been 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 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.
We investigate the properties of the Kitaev honeycomb model with both site dilution and exchange randomness. Embarking on this work, we review disorder in some strongly correlated electron systems, including spin-½ and spin-1 Heisenberg antiferromagnetic chains, two dimensional Heisenberg antiferromagnets, the cuprates and graphene. We outline some aspects of resonating valence bond phases, valence bond solids, spin liquids and quantum computation that are pertinent to an understanding of the Kitaev model. The properties of the Kitaev model without disorder are discussed and it is found to be a critical spin liquid, with algebraic correlations in two spin operators sigma^{alpha}_{i}sigma^{alpha}_{j}, where i and j are either end of a link of type alpha = x, y or z on the honeycomb lattice. The Kitaev model is exactly solvable and we show that this remains so in the presence of site dilution and exchange randomness. We find that vacancies bind a flux. In the gapped phase, a vacancy forms an effective paramagnetic moment. With two or more vacancies we describe the interaction of their effective moments and show that a finite density of vacancies leads to a divergent macroscopic susceptibility at small fields. In the gapless phase the effective moment has a susceptibility that is, to leading order at small fields, chi(h)~log(1/h). Interaction between the moments from two vacancies on opposite sublattices cuts off this divergence in susceptibility at a large but finite constant. Two vacancies on the same sublattice behave quite differently and we find the combined susceptibility is parametrically larger than that of an isolated vacancy, chi(h)sim [h(log(1/h))^{3/2}]^{-1}. We also investigate the effects of slowly varying, quenched disorder in exchange coupling. We demonstrate that this does not qualitatively affect the susceptibility but show that the heat capacity C ~ T^{2/z}, where z is a measure of the disorder and increases from one with increasing disorder strength.