宇田川 将文

We study the interplay of topological bottlenecks and energetic barriers to<br /> equilibration in a Coulomb spin liquid where a short-range energetic coupling<br /> between defects charged under an emergent gauge field supplements their<br /> entropic long-range Coulomb interaction. This work is motivated by the<br /> prevalence of memory effects observed across a wide range of geometrically<br /> frustrated magnetic materials, possibly including the spontaneous Hall effect<br /> observed in Pr2Ir2O7. Our model is canonical spin-ice model on the pyrochlore<br /> lattice, where farther-neighbour spin couplings give rise to a nearest-neighbor<br /> interaction between topological defects which can easily be chosen to be<br /> unnatural or not, i.e. attractive or repulsive between defects of equal gauge<br /> charge. Among the novel features of this model are the following. After<br /> applying a field quench, a rich dynamical approach to equilibrium emerges,<br /> dominated by multi-scale energy barriers responsible for long-lived<br /> magnetization plateaux. These even allow for the metastability of a<br /> &quot;fragmented&quot; spin liquid, an elusive regime where partial order co-exists with<br /> a spin liquid. Perhaps most strikingly, the attraction produces clusters of<br /> defects whose stability is due to a combination of energetic barriers for their<br /> break-up and proximity of opposite charges along with an entropic barrier<br /> generated by the topological requirement of annihilating a defect only together<br /> with an oppositely charged counterpart. These clusters may take the form of a<br /> &quot;jellyfish&quot; spin texture, comprising an arrangement of same-sign gauge-charges,<br /> centered on a hexagonal ring with branches of arbitrary length. The ring<br /> carries a clockwise or counterclockwise circular flow of magnetisation. This<br /> emergent toroidal degrees of freedom provides a possibility for time reversal<br /> symmetry breaking with possible relevance to the spontaneous Hall effect<br /> observed in Pr2Ir2O7.

Finite-temperature (T) properties of a Kitaev model defined on a honeycomb lattice are investigated by a quantum Monte Carlo simulation, from the viewpoint of fractionalization of quantum S = 1/2 spins into two types of Majorana fermions, itinerant and localized. In this system, the entropy is released successively at two well-separated T scales, as a clear indication of the thermal fractionalization. We show that the high-T crossover, which is driven by itinerant Majorana fermions, is closely related with the development of nearest-neighbor spin correlations. On the other hand, the low-T crossover originates in thermal fluctuations of fluxes composed of localized Majorana fermions, by which the spectrum of itinerant Majorana fermions is significantly disturbed. As a consequence, in the intermediate-T range between the two crossovers, the system exhibits T-linear behavior in the specific heat and coherent transport of Majorana fermions, which are unexpected for the Dirac semimetallic spectrum in the low-T limit. We also show that the flux fluctuations tend to open an energy gap in the Majorana spectrum near the gapless-gapped phase boundary. Our results indicate that the fractionalization is experimentally observable in the specific heat, spin correlations, and transport properties.

We study the entanglement spectrum of the Hubbard model at half filling on a kagome lattice. The entanglement spectrum is defined by the set of eigenvalues of a reduced thermal density matrix, which is naturally obtained in the framework of the dynamical mean-field theory. Adopting the cluster dynamical mean-field theory combined with continuous-time auxiliary-field Monte Carlo method, we calculate the entanglement spectrum for a three-site triangular cluster in the kagome Hubbard model. We find that the results at the three-particle sector well capture the qualitative nature of the system. In particular, the eigenvalue of the reduced density matrix, corresponding to the chiral degrees of freedom, exhibits a characteristic temperature scale T-chiral, below which a metallic state with large quasiparticle mass is stabilized. The entanglement spectra at different particle number sectors also exhibit characteristic changes around T-chiral, implying the development of inter-triangular ferromagnetic correlations in the correlated metallic regime.

A three-dimensional Kitaev model on a hyperhoneycomb lattice is investigated numerically at finite temperature. The Kitaev model is one of the solvable quantum spin models, where the ground state is given by gapped and gapless spin liquids, depending on the anisotropy of the interactions. This model can be rewritten as a free Majorana fermion system coupled with Z2 variables. The density of states of Majorana fermions shows an excitation gap in the gapped region, while it is semimetallic in the gapless region reflecting the Dirac node. Performing the Monte Carlo simulation, we calculate the temperature dependence of the Majorana spectra. We find that the semimetallic dip is filled as temperature increases in the gapless region, but surprisingly, the spectrum develops an excitation gap in the region near the gapless-gapped boundary. Such changes of the low-energy spectrum appear sharply at the transition temperature from the spin liquid to the paramagnetic state. The results indicate that thermal fluctuations of the Z(2) fields significantly influence the low-energy state of Majorana fermions, especially in the spin liquid formation.

Effects of an open surface on a magnetic Chern insulator are investigated in comparison with those of an interface to a capping magnetic layer. In magnets, an open surface often perturbs the magnetic order by a reconstruction of the magnetic moment directions near the surface. On the other hand, in topological insulators, it leads to the formation of topologically protected surface states. These two contrasting effects may coexist in magnetic Chern insulators, which give rise to nontrivial surface reconstruction. For instance, the chiral edge current is largely enhanced by the edge reconstruction in a two-dimensional magnetic Chern insulator realized in a quarter-filled Kondo lattice model on a triangular lattice. We here show that the edge reconstruction can be described semiquantitatively by a simple junction model between the bulk topological magnetic state and a ferromagnetic capping layer. We further clarify how the chiral edge current is affected by the magnetic structure in the capping layer. Our results indicate that the topological edge state can be controlled magnetically through the junctions.