Nonlocal Spin Correlation as a Signature of Ising Anyons Trapped in Vacancies of the Kitaev Spin Liquid.

In the Kitaev chiral spin liquid, Ising anyons are realized as Z_{2} fluxes binding Majorana zero modes, which, however, are thermal excitations with finite decay rates. On the other hand, a lattice vacancy traps a Z_{2} flux even in the ground state, resulting in the stable realization of a Majorana zero mode in a vacancy. We demonstrate that spin-spin correlation functions between two vacancy sites exhibit long-range correlation arising from the fractionalized character of Majorana zero modes, in spite of the strong decay of bulk spin correlations. Remarkably, this nonlocal spin correlation does not decrease as the distance between two vacancy sites increases, signaling Majorana teleportation. Furthermore, we clarify that the nonlocal correlation can be detected electrically via the measurement of nonlocal conductance between two vacancy sites, which is straightforwardly utilized for the readout of Majorana qubits. These findings pave the way to the measurement-based quantum computation with Ising anyons trapped in vacancies of the Kitaev spin liquid.

Phonon thermal Hall effect in a metallic spin ice.

It has become common knowledge that phonons can generate thermal Hall effect in a wide variety of materials, although the underlying mechanism is still controversial. We study longitudinal κxx and transverse κxy thermal conductivity in Pr2Ir2O7, which is a metallic analog of spin ice. Despite the presence of mobile charge carriers, we find that both κxx and κxy are dominated by phonons. A T/H scaling of κxx unambiguously reveals that longitudinal heat current is substantially impeded by resonant scattering of phonons on paramagnetic spins. Upon cooling, the resonant scattering is strongly affected by a development of spin ice correlation and κxx deviates from the scaling in an anisotropic way with respect to field directions. Strikingly, a set of the κxx and κxy data clearly shows that κxy correlates with κxx in its response to magnetic field including a success of the T/H scaling and its failure at low temperature. This remarkable correlation provides solid evidence that an indispensable role is played by spin-phonon scattering not only for hindering the longitudinal heat conduction, but also for generating the transverse response.

Theoretical scheme for finite-temperature dynamics of Kitaev's spin liquids.

In this article, we review the theoretical formulation of finite temperature dynamics of Kitaev's spin liquid. We present the exact analytical solution of the dynamical spin correlation function at the integrable limit of Kitaev's model, on the basis of (2018Phys. Rev. B98220404). By combining the analytical solution with the equilibrium classical Monte-Carlo scheme, we construct a formulation to access the finite temperature dynamics of Kitaev's spin liquid exactly, with a reasonable amount of computational cost. This formulation is based on the real-time representation, which enables us to directly access the experimental observables defined in real frequency, without analytical continuation. The real-time scheme is essential to capturing the resonant features of the spectrum accurately, which occurs e.g. in the chiral spin liquid phase with isolated Majorana zero modes. Accordingly, this scheme provides an effective approach to address the nature of fractional excitations in Kitaev's spin liquid. As an application, we address the detection of zero mode around the site vacancy through the local resonant spectrum and discuss how the character of Kitaev's spin liquid emerges in its dynamical signature.

Scanning Tunneling Microscopy as a Single Majorana Detector of Kitaev's Chiral Spin Liquid.

We propose a local detection scheme for the Majorana zero mode (MZM) carried by a vison in Kitaev's chiral spin liquid (CSL) using scanning tunneling microscopy (STM). The STM introduces a single Majorana into the system through hole-charge injection and the Majorana interacts with the MZM to form a stable composite object. We derive the exact analytical expression of single-hole Green's function in the Mott insulating limit of Kitaev's model, and show that the differential conductance has split peaks, as a consequence of resonant tunneling through the vison-hole composite. The peak splitting turns out comparable to the Majorana gap in CSL, well within the reach of experimental observation.

Spectrum of Itinerant Fractional Excitations in Quantum Spin Ice.

We study the quantum dynamics of fractional excitations in quantum spin ice. We focus on the density of states in the two-monopole sector, ρ(ω), as this can be connected to the wave-vector-integrated dynamical structure factor accessible in neutron scattering experiments. We find that ρ(ω) exhibits a strikingly characteristic singular and asymmetric structure that provides a useful fingerprint for comparison to experiment. ρ(ω) obtained from the exact diagonalization of a finite cluster agrees well with that, from the analytical solution of a hopping problem on a Husimi cactus representing configuration space, but not with the corresponding result on a face-centered cubic lattice, on which the monopoles move in real space. The main difference between the latter two lies in the inclusion of the emergent gauge field degrees of freedom, under which the monopoles are charged. This underlines the importance of treating both sets of degrees of freedom together, and it presents a novel instance of dimensional transmutation.

Clustering of Topological Charges in a Kagome Classical Spin Liquid.

Fractionalization is a ubiquitous phenomenon in topological states of matter. In this work, we study the collective behavior of fractionalized topological charges and their instabilities, through the J_{1}-J_{2}-J_{3} Ising model on a kagome lattice. This model can be mapped onto a Hamiltonian of interacting topological charges under the constraint of Gauss' law. We find that the recombination of topological charges gives rise to a yet unexplored classical spin liquid. This spin liquid is characterized by an extensive residual entropy, as well as the formation of hexamers of same-sign topological charges. The emergence of hexamers is reflected by a half-moon signal in the magnetic structure factor, which provides a signature of this new spin liquid in elastic neutron-scattering experiments. To study this phase, a worm algorithm has been developed which does not require the usual divergence-free condition.

Vaporization of Kitaev spin liquids.

The quantum spin liquid is an exotic quantum state of matter in magnets. This state is a spin analog of liquid helium that does not solidify down to the lowest temperature due to strong quantum fluctuations. In conventional fluids, the liquid and gas possess the same symmetry and adiabatically connect to each other by bypassing the critical end point. We find that the situation is qualitatively different in quantum spin liquids realized in a three-dimensional Kitaev model; both gapless and gapped quantum spin liquid phases at low temperatures are always distinguished from the high-temperature paramagnet (spin gas) by a phase transition. The results challenge the common belief that the absence of thermodynamic singularity down to the lowest temperature is a symptom of a quantum spin liquid.

Hidden multiple-spin interactions as an origin of spin scalar chiral order in frustrated Kondo lattice models.

We reveal the significance of kinetic-driven multiple-spin interactions hidden in geometrically frustrated Kondo lattice models. Carefully examining the perturbation in terms of the spin-charge coupling up to the fourth order, we find that a positive biquadratic interaction is critically enhanced and plays a crucial role on stabilizing a spin scalar chiral order near 1/4 filling in a triangular lattice case. This is a generalized Kohn anomaly, appearing only when the second-order perturbation is inefficient because of the degeneracy under frustration. The mechanism is potentially common to frustrated spin-charge coupled systems, leading to emergence of unusual magnetic orders.

Non-Kondo mechanism for resistivity minimum in spin ice conduction systems.

We present a mechanism of resistivity minimum in conduction electron systems coupled with localized moments, which is distinguished from the Kondo effect. Instead of the spin-flip process in the Kondo effect, electrons are elastically scattered by local spin correlations which evolve in a particular way under geometrical frustration as decreasing temperature. This is demonstrated by the cellular dynamical mean-field theory for a spin-ice-type Kondo lattice model on a pyrochlore lattice. Peculiar temperature dependences of the resistivity, specific heat, and magnetic susceptibility in the non-Kondo mechanism are compared with the experimental data in metallic Ir pyrochlore oxides.

Quantum melting of charge ice and non-Fermi-liquid behavior: an exact solution for the extended Falicov-Kimball model in the ice-rule limit.

An exact solution is obtained for a model of itinerant electrons coupled to ice-rule variables on the tetrahedron Husimi cactus, an analogue of the Bethe lattice of corner-sharing tetrahedra. It reveals a quantum critical point with the emergence of non-Fermi-liquid behavior in melting of the "charge ice" insulator. The electronic structure is compared with the numerical results for the pyrochlore-lattice model to elucidate the physics of electron systems interacting with the tetrahedron ice rule.

Partial Kondo screening in frustrated Kondo lattice systems.

We investigate the effect of geometrical frustration on the competition between the Kondo coupling and the Ruderman-Kittel-Kasuya-Yosida interaction in Kondo lattice systems. By variational Monte Carlo simulations, we reveal an emergent quantum phase with partial ordering in which the frustration is relieved by forming a magnetic order on a sublattice and leaving the rest in the Kondo screening with spin-singlet formation. The role of quantum fluctuations and spin-charge interplay is elucidated.

Chirality-driven mass enhancement in the kagome Hubbard model.

We investigate the quasiparticle-mass enhancement in the Hubbard model on the frustrated kagome lattice by using a cluster extension of the dynamical mean-field theory. By analyzing the cluster density matrix, we find a hierarchy of energy scale among charge, spin, and chirality degrees of freedom. A large amount of entropy associated with the chirality is released at a much lower temperature than other energy scales for spin and charge fluctuations, leading to a sharp peak in the specific heat and the single-particle spectrum. The results manifest a generic mechanism of mass enhancement driven by an emergent composite degree of freedom under geometrical frustration.

Charge ordering and coexistence of charge fluctuations in quasi-two-dimensional organic conductors theta-(BEDT-TTF)2X.

We present a scenario for the peculiar coexistence of charge fluctuations observed in quasi-2D 1/4-filled organic conductors theta-(BEDT-TTF)2X in the quantum critical regime where the charge ordering is suppressed down to zero temperature. The scenario is explored in the extended Hubbard model including electron-phonon couplings on an anisotropic triangular lattice. We find that the coexisting fluctuations emerge from two different instabilities, the "Wigner crystallization on a lattice" driven by the off-site Coulomb repulsion and the charge-density-wave formation due to the nesting of the Fermi surface, not from phase competition or real-space inhomogeneity. This mechanism explains the contrastive temperature dependence of two fluctuations in experiments.