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Register a new userEquivalence between vortices, twists and chiral gauge fields in Kitaevs honeycomb lattice model
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We demonstrate that $mathbb{Z}_2$ gauge transformations and lattice deformations in Kitaevs honeycomb lattice model can have the same description in the continuum limit of the model in terms of chiral gauge fields. The chiral gauge fields are coupled to the Majorana fermions that satisfy the Dirac dispersion relation in the non-Abelian sector of the model. For particular values, the effective chiral gauge field becomes equivalent to the $mathbb{Z}_2$ gauge field, enabling us to associate effective fluxes to lattice deformations. Motivated by this equivalence, we consider Majorana-bounding $pi$ vortices and Majorana-bounding lattice twists and demonstrate that they are adiabatically connected to each other. This equivalence opens the possibility for novel encoding of Majorana-bounding defects that might be easier to realise in experiments.
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Magnetic skyrmions are stable topological spin textures with significant potential for spintronics applications. Merons, as half-skyrmions, have been discovered by recent observations, which have also raised the upsurge of research. The main purpose of this work is to study further the lattice forms of merons and skyrmions. We study a classical spin model with Dzyaloshinskii-Moriya interaction, easy-axis, and in-plane magnetic anisotropies on the honeycomb lattice via Monte Carlo simulations. This model could also describe the low-energy behaviors of a two-component bosonic model with a synthetic spin-orbit coupling in the deep Mott insulating region or two-dimensional materials with strong spin-orbit coupling. The results demonstrate the emergence of different sizes of spiral phases, skyrmion and vortex superlattice in absence of magnetic field, furthered the emergence of field-induced meron and skyrmion superlattice. In particular, we give the simulated evolution of the spin textures driven by the magnetic field, which could further reveal the effect of the magnetic field for inducing meron and skyrmion superlattice.
Quantum phase transitions in the Hubbard model on the honeycomb lattice are investigated in the variational cluster approximation. The critical interaction for the paramagnetic to antiferromagnetic phase transition is found to be in remarkable agreement with a recent large-scale quantum Monte Carlo simulation. Calculated staggered magnetization increases continuously with $U$ and thus we find the phase transition is of a second order. We also find that the semimetal-insulator transition occurs at infinitesimally small interaction and thus a paramagnetic insulating state appears in a wide interaction range. A crossover behavior of electrons from itinerant to localized character found in the calculated single-particle excitation spectra and short-range spin correlation functions indicates that an effective spin model for the paramagnetic insulating phase is far from a simple Heisenberg model with a nearest-neighbor exchange interaction.
Superpositions of spin helices can yield topological spin textures, such as two-dimensional vortices and skyrmions, and three-dimensional hedgehogs. Their topological nature and spatial dimensionality depend on the number and relative directions of the constituent helices. This allows mutual transformation between the topological spin textures by controlling the spatial anisotropy. Here we theoretically study the effect of anisotropy in the magnetic interactions for an effective spin model for chiral magnetic metals. By variational calculations for both cases with triple and quadruple superpositions, we find that the hedgehog lattices, which are stable in the isotropic case, are deformed by the anisotropy, and eventually changed into other spin textures with reduced dimension, such as helices and vortices. We also clarify the changes of topological properties by tracing the real-space positions of magnetic monopoles and antimonopoles as well as the emergent magnetic field generated by the noncoplanar spin textures. Our results suggest possible control of the topological spin textures, e.g., by uniaxial pressure and chemical substitution in chiral materials.
It is widely accepted that topological superconductors can only have an effective interpretation in terms of curved geometry rather than gauge fields due to their charge neutrality. This approach is commonly employed in order to investigate their properties, such as the behaviour of their energy currents. Nevertheless, it is not known how accurately curved geometry can describe actual microscopic models. Here, we demonstrate that the low-energy properties of the Kitaev honeycomb lattice model, a topological superconductor that supports localised Majorana zero modes at its vortex excitations, are faithfully described in terms of Riemann-Cartan geometry. In particular, we show analytically that the continuum limit of the model is given in terms of the Majorana version of the Dirac Hamiltonian coupled to both curvature and torsion. We numerically establish the accuracy of the geometric description for a wide variety of couplings of the microscopic model. Our work opens up the opportunity to accurately predict dynamical properties of the Kitaev model from its effective geometric description.
e provide a detailed analysis of a topological structure of a fermion spectrum in the Hofstadter model with different hopping integrals along the $x,y,z$-links ($t_x=t, t_y=t_z=1$), defined on a honeycomb lattice. We have shown that the chiral gapless edge modes are described in the framework of the generalized Kitaev chain formalism, which makes it possible to calculate the Hall conductance of subbands for different filling and an arbitrary magnetic flux $phi$. At half-filling the gap in the center of the fermion spectrum opens for $t>t_c=2^{phi}$, a quantum phase transition in the 2D-topological insulator state is realized at $t_c$. The phase state is characterized by zero energy Majorana states localized at the boundaries. Taking into account the on-site Coulomb repulsion $U$ (where $U<<1$), the criterion for the stability of a topological insulator state is calculated at $t<<1$, $t sim U$. Thus, in the case of $ U > 4Delta $, the topological insulator state, which is determined by chiral gapless edge modes in the gap $Delta$, is destroyed.
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