Our results pave the way for novel electronic ordering, transport, and magnetoelectric phenomena induced by local parity mixing. Hayami, H. Kusunose, and Y. Motome, Kotai Butsuri 50, S. B 90 , R S. B 90 , [Editors' Suggestion].

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## Quantum spin liquid at finite temperature: Proximate dynamics and persistent typicality

Noncoplanar magnetic order and 3D massless Dirac electrons on a cubic lattice Noncoplanar multiple-Q orders, which are characterized by more than a single ordering wave vector, often lead to topologically nontrivial states and new low-energy excitations. To explore the possibility of such multiple-Q orders on unfrustrated lattices, we investigate noncoplanar magnetic orders on a simple cubic lattice. As a result, we find that a triple-Q magnetic order on the cubic lattice significantly affects the low-energy single-particle spectrum, resulting in the three-dimensional massless Dirac electrons.

We also show that such magnetic ordering possesses gapless surface states, becomes a Weyl semimetal in an applied magnetic field, and changes into a topological insulator by an appropriate perturbation. Moreover, we examine the stability of the triple-Q state by mean-field calculations and Monte Carlo simulation for itinerant electron models, such as the Kondo lattice model and the periodic Anderson model.

Our results indicate that the itinerant nature of electrons, rather than the geometrical frustration, plays an important role in realizing noncoplanar magnetic orders. Hayami, T. Misawa, Y. Yamaji, and Y. B 89 , S. Misawa, and Y. Motome, JPS Conf. Spin-orbital frustration in pyrochlore molybdenum oxides Pyrochlore molybdenum oxides A 2 Mo 2 O 7 provide a fertile ground for studying metal-insulator transitions and associated unconventional magnetic phenomena. In the insulating materials, a long-range magnetic order is suppressed, and at low temperatures a spin glass behavior appears with frozen magnetic moments in random directions.

It has long been believed that the absence of long-range ordering is due to the geometrical frustration between isotropic antiferromgnetic exchnge couplings on the pyrochlore lattice. Recently, however, the neutron scattering experiment for a single crystal of Y 2 Mo 2 O 7 has revealed an unexpected behavior, that is, the existence of weak ferromagnetic spin fluctuations. This urges reconsideration of the microscopic origin of the spin glass behavior.

Performing the state-of-the-art first-principles calculations including the relativistic spin-orbit coupling, we clarified that the ground state suffers from keen competition between antiferromagnetic and ferromagnetic states. Furthermore, through the analyses of localized spin model and multi-orbital Hubbard model, we found that the magnetic competition couples with the competition between different orbital orders via the spin-orbit coupling. The new picture of magnetic frustration originating from the orbital degrees of freedom well explains the experimental results.

Shinaoka, Y. Motome, T. Miyake, and S. Ishibashi, Phys. B 88 , [selected in Kaleidoscope ]. Charge order in Kondo lattice systems The Kondo lattice model, in which conduction electrons couple with localized quantum spins, is one of the most fundamental models for heavy fermion systems. The model has been intensively studied for searching for novel quantum phases. In particular, the possibility of a charge ordered phase has been examined for more than 30 years, but it was not clarified except for the special cases in one and infinite dimensions.

Utilizing two sophisticated numerical methods, a cluster extension of the dynamical mean-field theory and a multi-variables variational Monte Carlo method, we solve this problem and show the evidence of charge ordering in two dimensions. Furthermore, we find that the local Kondo singlet formation plays a key role in stabilizing the charge order. Our results indicate that the charge order in the Kondo lattice systems is qualitatively different from those by intersite Coulomb repulsion. We extend the study to three-dimensional systems, and find that the charge order appears with a noncoplanar magnetic ordering due to the effective frustration under the charge order.

Misawa, J. Yoshitake, and Y. Quantum anomalous Hall effect in kagome ice Spin ice exhibits a peculiar magnetization plateau under the [] magnetic field. It is considered to be realized by forming a spin liquid state called kagome ice on the [] kagome planes. For clarifying the effect of the locally-correlated kagome ice on itinerant electrons, we investigate numerically the electronic and transport properties of the spin-ice type Kondo lattice model on a kagome lattice.

As a result, we find that the kagome ice spin correlation opens a charge gap in the electronic state in spite of absence of magnetic long-range order. Moreover, the insulating state is a quantum anomalous Hall insulator with a quantization of the Hall conductivity. As increasing magnetic field, the charge gap closes, but opens again in the fully-polarized insulating state, in which the Hall conductivity is quantized at a different value. We show that this is considered as a transition between different topological insulators.

Ishizuka and Y. B 87 , R Dirac half-metal in a triangular ferrimagnet A monolayer of carbon, graphen, has attracted much interest because of the Dirac electrons with a peculiar linear dispersion in the electronic state. However, it has some difficulty for application to spintronics as the spin-orbit coupling is very weak. We here theoretically propose a possibility of the Dirac electrons from a different point of view.

Considering a triangular magnet with itinerant electrons, we show that the Dirac electronic state with a linear dispersion emerges in underlying three-sublattice ferrimagnetic order. The Dirac electrons are perfectly spin-polarized, i. Furthermore, by Monte Carlo simulation, we clarify the parameter region where the Dirac half-metallic phase is stabilized. The discovery of such new Dirac electrons will stimulate further development of spintronics. Metallic partial disorder in a periodic Anderson model on a triangular lattice In our previous studies, we found the partially disordered states in the Kondo lattice model, periodic Anderson model, and Ising Kondo lattice model on a triangular lattice.

The partially disordered states, however, are all insulating with a finite charge gap. Meanwhile, the partially disordered states in experiments are metallic. It is therefore important to find a metallic partial disorder theoretically for providing understanding of the experiments. Here, we extend the mean-field analysis of the periodic Anderson model to other commensurate fillings and carrier-doped regions around them.

As a result, we find that a different type of partial disorder emerges at other commensurate fillings, and that hole doping induces a metallic partially disordered state. Hayami, M. Partial disorder in an Ising-spin Kondo lattice model on a triangular lattice The triangular-lattice Ising model, a fundamental model for geometrically frustrated systems, exhibits macroscopic degeneracy in the ground state when the interactions are restricted to nearest neighbors and antiferromagnetic. A nontrivial emergent state from this degeneracy is a partial disorder, which is coexistence of magnetic order and paramagnetic moments.

In two dimensions, however, the partial disorder is fragile against thermal fluctuations, and does not form a long-range order. Stimulated by recent experimental findings of a partial disorder in quasi-two-dimensional conducting systems, we explore the possibility of partial disorder by the interaction between localized moments and itinerant electrons. By studying an Ising-spin Kondo lattice model on a triangular lattice by Monte Carlo simulation, we found that a partial disorder is stabilized even in two dimensions in the spin-charge coupled system. We clarified that the charge degree of freedom plays a crucial role in the emergence of partial disorder through an electronic phase separation, charge ordering, and opening of the charge gap.

B 87 , H. Hidden multiple-spin interactions in frustrated itinerant-electron systems Anomalous Hall effect by spin scalar chiral ordering has attracted much attention. This state, however, is not explained by the previously-known scenario of the nesting of Fermi surface, and hence, the origin was unclear.

We here investigate the stabilization mechanism by carefully examining the perturbation in terms of the spin-charge coupling up to fourth order. As a result, we found that the effective exchange interactions in the second order RKKY interactions are degenerate due to the frustration, and that the higher fourth-order contributions play a decisive role. Among many effective multiple-spin interactions in the fourth order, the biquadratic interaction is critically enhanced with a positive coefficient.

This is not due to the nesting but a Fermi surface connection, which we call the generalized Kohn anomaly. Our results suggest that the nontrivial stabilization mechanism is hidden in the wide range of frustrated itinerant electron systems. Akagi, M. Resistivity minimum in spin-ice conduction systems In frustrated magnets called spin ice, a long-range magnetic order is suppressed and a spin-liquid like state can emerge with showing only local spin correlations obeying the so-called ice rule.

When such peculiar spatial magnetic texture interacts with itinerant electrons, one can expect some new transport phenomena. We here consider this problem in a model in which spin-ice type Ising moments are coupled with itinerant electrons on a pyrochlore lattice, by employing a cluster extension of the dynamical mean-field theory. As a result, we found that, in low electron density region, the system exhibits a spin-ice like liquid state, and more importantly, the electrical resistivity shows a minimum corresponding to the development of local spin correlations.

This clearly shows that the special ice-rule correlation becomes a strong scatterer of electrons, giving a completely new mechanism of resistivity minimum distinct from the conventional Kondo effect. The results suggest the possibility of understanding the resistivity minimum recently observed in some Ir pyrochlore oxides. Udagawa, H. Ishizuka, and Y.

Partial disorder in the periodic Anderson model on a triangular lattice In Kondo lattice systems, geometrical frustration has recently attracted much interest as a new control parameter to induce novel quantum states in the competition between the RKKY interaction and Kondo coupling. In particular, a partial disordered PD state was suggested both experimentally and theoretically, in which a magnetic order appears only on a subset of sublattices so as to relieve the frustration; however, its basic properties as well as the stabilization mechanism remain unclear.

We here investigate the ground state of a fundamental model for the Kondo lattice systems, i. We found that a PD state is stabilized concomitant with charge ordering between a degree AF metal and a Kondo insulator in the region from weak to intermediate correlation, and that the PD state is insulating and shows a characteristic crossover in the electronic structure.

From a comparison to the previous results for the Kondo lattice models, it is clarified that the charge degree of freedom of localized electrons plays a crucial role in stabilizing PD. Metal-insulator transition in charge-frustrated systems under ice-rule local constraint Ice rule, which is a local constraint named after the configuration of protons in water ice, appears also in the charge configuration in frustrated charge-ordering systems. Transport properties in such charge-frustrated systems have attracted attention both experimentally and theoretically, but detailed understanding is not obtained so far.

We here examine this problem by investigating electronic and transport properties for an extended Falicov-Kimball model on various frustrated lattice structures, in which the configuration of localized particles obeys the ice rule. In particular, in the model on the pyrochlore lattice, the system shows a phase transition from a metal to the charge-ice insulator without entering into the Anderson insulator that is seen in the case with random configuration.

These novel behaviors are considered to originate from the particular spatial correlation due to the gauge structure hidden in the ice-rule systems. Ishizuka, M. B 83 , Spin glass transition and spin-lattice coupling in pyrochlore antiferromagnets Many frustrated magnets exhibit a spin glass state at low temperatures.

Usually the spin glass is induced by randomness, however, in several pyrochlore magnets, a spin glass transition takes place even in a best-quality sample with virtually disorder free, and furthermore, the transition temperature is almost independent of the strength of disorder. To explore the origin of these peculiar behaviors, we investigate the effect of spin-lattice coupling in a bond-disordered pyrochlore Heisenberg antiferromagnet by extensive Monte Carlo simulations. As a result, we find that the spin glass transition temperature is strongly enhanced by the spin-lattice coupling, and remarkably, becomes almost constant in a wide range of the strength of disorder.

This is presumably because the spin-lattice coupling enhances the spin collinearity and suppresses thermal fluctuations. The spin glass transition is of second order and its critical properties are compatible with the conventional ones. Our results well account for the puzzling behaviors observed in experiments. Tomita, and Y. B 90 , H. Shinaoka and Y. B 82 , H. Spin scalar chirality ordering and anomalous Hall effect in triangular-lattice ferromagnetic Kondo models Recently, spin scalar chirality has attracted much attention as a novel origin of the anomalous Hall effect AHE , independent of the relativistic spin-orbit coupling.

In fact, it was pointed out that AHE is induced by noncoplanar magnetic orders on the kagome or triangluar lattice.

However, in the previous studies, such magnetic orders were given by hand with neglecting effects of itinerant electrons, and their stability relative to other orders was not examined. In the present study, we investigate the ground state of the ferromagnetic Kondo model on the triangular lattice by variational calculations for various magnetic states up to four-sublattice orders. We also compute the Hall conductivity in these chiral phases, which is quantized according to the Chern number in gapped insulating states.

Akagi and Y. Partial Kondo screening in frustrated Kondo lattice systems One of the most important concepts in Kondo lattice systems is competition between the Kondo coupling and the RKKY interaction. The competition leads to a quantum critical point QCP between a magnetically-ordered state and a Fermi liquid state, and furthermore, it is the origin of novel phenomena around the QCP, such as a non-Fermi liquid behavior and a superconductivity. To explore a new quantum phase related to the competition, we investigate the ground state of geometrically-frustrated Kondo lattice systems by employing a high-precision variational Monte Carlo simulation.

We find that a partially-ordered state, in which a magnetic order and a Kondo spin singlet coexists, emerges between a magnetically-ordered state stabilized by the RKKY interaction and a Kondo spin liquid state stabilized by the Kondo coupling. We clarified that this new quantum phase is stabilized by quantum fluctuations as well as magnetic anisotropy, and that it is accompanied by a charge disproportionation.

Motome, K. Nakamikawa, Y. Yamaji, and M. Udagawa, Phys. Motome, Y. Udagawa, J. A, SA Quantum melting of charge-ice insulator and non-Fermi-liquid behavior Ice rule is a local constraint observed in a broad range of condensed matter, such as the proton position in water ice and the Ising spin configuration in spin ice. This local constraint is not enough to let the system ordered, and the ground state often retains macroscopic degeneracy. However, the disordered state is not completely random but has a specific spatial correlation due to a hidden gauge structure.

To clarify the effect of special correlations on itinerant electrons, we consider an extended Falicov-Kimball model which describes a correlation between ice-rule localized particles and itinerant electrons, and find an exact solution of this model on a loopless tetrahedron Husimi cactus. We show that the system becomes a charge-ice insulator with 1D-like electronic structure in large correlation regime, and that non-Fermi-liquid behavior appears at the quantum critical point where the charge ice melts.

Chirality-driven heavy-mass behavior Heavy-mass behavior in transition metal compounds, such as spinel oxide LiV 2 O 4 , has attracted much attention, but its origin still remains unclear. Focusing on the synergy between strong electron correlation and geometrical frustration, we investigate the kagome Hubbard model by employing a cluster extension of the dynamical mean-field theory and the continuous-time quantum Monte Carlo simulation.

From the detailed analysis of the cluster density matrix, we find that the system exhibits a hierarchy in the energy scale among charge, spin, and chirality degrees of freedom, and the chirality becomes dominant at the lowest temperature. Furthermore, by calculating the specific heat and entropy, we clarify that heavy-mass behavior emerges from a large amount of entropy associated with the chirality. These results indicate that the frustration plays not only a secondary role just to suppress long-range ordering but also an intensive role to invoke a novel electronic state through a formation of multiple degree of freedom such as chirality.

Udagawa and Y. Chou 5. The double-perovskites exhibit many fundamentally interesting chemical and physical properties; they can have electronic structures raging from insulator, metallic, halfmetallic to superconductor; they can also have different magnetic order parameters; or even simultaneously containing the multiple order parameters, such as multiferroicity. Using a modified floating zone growth method, we are able to grow the high-quality single crystal of YBCFO for the detailed studies using neutron scattering.

This incommensurate phase develops into a spiral spin ordering with a propagating vector along c-axis. This finding also calls for the analytically modeling for the further understanding the mechanism behind. We propose many-body invariants for multipolar higher-order topological insulators by generalizing Resta's pioneering work on polarizations. The many-body invariants are designed to measure the distribution of electron charge in unit cells and thus can detect quantized multipole moments purely from the bulk ground state wavefunctions.

Using the invariants, we prove the bulk-boundary correspondence of the higher-order topological insulators. Further, we show that our invariants can diagnose the corner charge of rotational- symmetric crystalline insulators. Application of our invariants to spin systems as well as various other aspects of the many-body invariants will be discussed. We have argued that these compounds might contain significant amount of effective quenched randomness or inhomogeneity of varying origin: either of external origin such as the substitution disorder, or of internal origin dynamically self-generated via the coupling to other degrees of freedom in solids such as the charge, the lattice and the orbital.

The results are discussed in connection with a variety of experimentally observed QSL materials, which seem to provide a consistent explanation of many recent experimental observations. Watanabe, H. Kawamura, H. Nakano and T. Sakai, J. Kawamura, K. Watanabe and T. Shimokawa, J. Shimokawa, K. Watanabe and H. Kawamura, Phys Rev. B 92 , Uematsu and H. Kawamura, J. Kawamura, Phys. B 98 , Since Haldane conjectured that ground state of one-dimensional Heisenberg antiferromagnet has a finite spin excitation gap for integer spins or gapless excitations for half-odd integer spins, it has inspired lots of theoretical and experimental studies on the low-dimensional quantum magnets.

Comprehensive magnetic, elastic, and thermal properties have been studied in single crystalline as well as polycrystalline NiTe 2 O 5. In this presentation, we present physical properties of NiTe 2 O 5 compound and discuss thermodynamic behavior associated with the order parameter. A fundamental motif in frustrated magnetism is the tetrahedral cluster -- four spins with each pair separated by the same distance.

If the spins are coupled by Heisenberg couplings, they must add to zero to minimize energy. This leads to a simple mathematical criterion for classical ground states -- we have four vectors which are constrained to add to zero. We show that this leads to a five-dimensional space of allowed states. Remarkably, this space has 'non-manifold' structure. It contains 'singular' points about which it appears to be six dimensional.

We use this construction to build a semi-classical theory for the tetrahedral cluster. In the low-energy limit, it takes a very simple form. It decomposes into two independent objects -- a rigid rotor a spinning top and a free spin. This free spin is perhaps the simplest example of an 'emergent' quantity, arising from angular variables in the spin configuration. This provides an elegant way to understand the energy spectrum and physical properties of tetrahedral molecular magnets. Spin-orbit coupling plays a very important role in several problems of condensed matter physics, especially in the spin-orbit entangled j-state.

The conventional wisdom in the community is that in order to realize the j-physics one needs to look at compounds with heavier elements like Ir. In this talk, I will challenge this wisdom and demonstrate how some of Cu oxides can host j-physics despite the smaller spin-orbit coupling [1]. Gapontsev, Sergey V. Streltsov, Daniel I.

Magnetic systems are characterised by microscopic interaction strengths that couple magnetic moments of different atomic sites. Depending on the magnitudes, signs and ranges of these interactions, various magnetic ground states can be realised, the simplest examples being various collinear magnetic arrangements.

We have been probing several new systems that are likely candidates of this class of compounds.

I shall discuss some of these systems in my presentation. The search for quantum spin -orbital liquids QSL -materials where local moments are well formed but continue to fluctuate quantum mechanically down to zero temperature still remains a fundamental challenge in condensed matter physics.

## Experimental identification of quantum spin liquids

In this talk, we shall show that the electronic structure of 6H perovskite type quaternary iridates Ba 3 MIr 2 O 9 , have all the necessary ingredients to host QSL state. In Ba 3 MIr 2 O 9 , Ir ions form structural dimers and non-magnetic M provides a knob to tailor the valence of Ir leading to emergent quantum phases. As a first example [1], we shall consider the pentavalent d 4 6H perovskite iridate Ba 3 ZnIr 2 O 9 and argue that the ground state of this system is a realization of novel spin-orbital liquid state.

While the Ir ions within the structural Ir2O9 dimer prefers to form a spin-orbit singlet states SOS with no resultant moment, however substantial frustrated inter-dimer exchange interactions induce quantum fluctuations in the SOS states favoring spin-orbital liquid phase at low enough temperature. As a second example [2] we shall consider the d 4. We shall also discuss the importance of Kitaev interactions in the realization QSL phases for the d 5 members of the same family[3].

Finally we shall compare our results with d 3 [4] and d 4 [5] Ir based double perovskites, particularly explain the origin of moments and presence of spin-orbital singlets in Ba 2 YIrO 6. With this solution, we will address how local disturbance of the system, such as impurity, manifests itself in the thermodynamic and dynamical properties, in association with the nature of fractionalized excitations. In particular, we will focus on the Vison zero-energy state appearing around the site vacancy, and discuss how to observe it experimentally.

Changlani et al. Lett , ] -- a result that holds for arbitrary magnetization -- we develop an exact mapping between its exact quantum three-coloring wavefunctions and the characteristic localized and topological magnons. This map, involving resonating two-color loops, is developed to represent exact many-body ground state wavefunctions for special high magnetizations.

For the case of zero magnetization, where the ground state is not exactly known, we perform density matrix renormalization group calculations. The recent discovery of topological semimetals, which possess distinct electron-band crossing with non-trivial topological characteristics, has stimulated intense research interest. By extending the notion of symmetry-protected band crossing into one of the simplest magnetic groups, namely by including the symmetry of time-reversal followed by space-inversion, we predict the existence of topological magnon-band crossing in three-dimensional 3D antiferromagnets.

The crossing takes the forms of Dirac points and nodal lines, in the presence and absence, respectively, of the conservation of the total spin along the ordered moments. Inelastic neutron scattering experiments have been carried out to detect the bulk magnon-band crossing in a single-crystal sample. The highly interconnected nature of the spin lattice suppresses quantum fluctuations and facilitates our experimental observation, leading to remarkably clean experimental data and very good agreement with the linear spin-wave calculations. The predicted topological Dirac points are confirmed [2].

Li et al. Yao et al. The search for topological insulators has been actively promoted in the field of condensed matter physics. Recently, the concept of topologically insulating state and associated edge states have been extended to bosonic quasiparticles, such as magnons in solids [1, 2]. A color contour map of the scattering intensities is shown in Fig. The two dispersive branches correspond to the band which is dispersive along both H and K directions.

In addition, the decrease in intensity was observed at 2. The correspondence indicates the presence of thermally excited topologically protected edge states induced by a bipartite nature of the lattice [6]. Shindou, R. Matsumoto, S. Murakami, J. Ohe, Phys. B 87 Su, J. Schrieffer and A. Heeger, Phys. Although the low energy fractional excitations of one-dimensional integrable models are often well-understood, exploring quantum dynamics in these systems remains challenging in the gapless regime, especially at intermediate and high energies.

Various excitations at different energy scales are identified crucial to the dynamic spin structure factors under the guidance of sum rules. At small magnetic polarization, gapless excitations of psinons and antipsinons dominate the low energy spin dynamics. In contrast, spin dynamics at intermediate and high energies is characterized by the two- and three-string states. The dynamic spectra of the identified dominant excitations evolve with clear energy separations when tuning the magnetic field, conveying a simple and straightforward way to clearly identify the novel string excitations in proper condensed matter systems.

Our predictions have been experimentally confirmed on the quasi-one-dimensional material SrCo2V2O8, where the details of the experimental observations will also be discussed. Topological spin texture consisting of multiple-q spin spiral is of great interest for novel quantum transport phenomena and spintronic functions. A recent interesting example is a magnetic skyrmion, which is a topologically stable, vortex-like spin object discovered in noncentrosymmetric systems allowing the Dzyaloshinskii-Moriya DM interaction [1,2].

The title compound SrFeO 3 is a promising candidate of the centrosymmetric compound hosting a novel skyrmion lattice in the absence of the DM interaction. SrFeO 3 has been known as a rare oxide showing both helimagnetism and metallic conduction while preserving the centrosymmetric cubic lattice. While the magnetic ground state has been believed to be a simple proper-screw-type spin order for long time, we have found that the magnetic phase diagram of SrFeO 3 hosts a rich variety of helimagnetic phases, two of which show novel topological helimagnetic orders [3].

In this presentation, I will show the topologically nontrivial helimagnetic phases in the simple cubic perovskite SrFeO 3 , which were discovered by the polarized and unpolarized small angle neutron scattering SANS measurements on the single crystalline samples. We found that SrFeO 3 shows two kinds of multiple-q helimagnetic structures: an anisotropic double-q spin spiral and an isotropic quadruple-q spiral hosting a three-dimensional lattice of topological singularities [4]. As a related topic, our recent discovery of a novel helimagnetic phase in the isostructural cubic perovskite Sr 1-x Ba x CoO 3 by Sakai et al.

These perovskite-type oxides not only diversify the family of SkX host materials, but furthermore provides an experimental missing link between centrosymmetric lattices and topological helimagnetic order. This work was done in collaboration with T. Nakajima, J. Kim, D. Inosov, Y. Tokunaga, S. Seki, N. Kanazawa, Y. Long, Y. Kaneko, R. George, K. Seemann, J. White, J. Gavilano, Y. Taguchi, T. Arima, B. Keimer, and Y. Seki, X. Yu, S. Ishiwata, and Y. Tokura, Science , Ishiwata et al.

B 84 , Sakai et al. Geometrical lattice engineering GLE has been presented as another potential way in recent times to realize novel topological and quantum many-body states. The key idea behind the GLE is to design fully epitaxial fully epitaxial ultra-thin heterostructures with an artificial lattice geometry e. As a prototype example of such interface and lattice engineering, I will talk about our ongoing work on rare earth nickelate heterostructures.

Middey et al. B 98 , ; Appl. The magnetic field response of the Mott-insulating honeycomb iridate Na 2 IrO 3 is investigated using torque magnetometry measurements in magnetic fields up to 60 tesla. Using exact diagonalization calculations, we show that such a distinctive signature in the torque response constrains the effective spin models for these classes of Kitaev materials to ones with dominant ferromagnetic Kitaev interactions, while alternative models with dominant antiferromagnetic Kitaev interactions are excluded.

We further show that at high magnetic fields, long range spin correlation functions decay rapidly, signaling a transition to a long-sought-after field-induced quantum spin liquid beyond the peak-dip structure. Stabilized alternatively are quantum disordered states called the spin liquid or unusual long-range orders having emergent degrees of freedom such as chirality or topological excitations.

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Extensive theoretical studies have proposed fascinating states of matter in various classes of models with frustration, and experimental studies have been undertaken to search for related exotic phenomena in real candidate compounds. However, there are numerous obstacles to clarify the frustration physics: the selection of a ground state from macroscopically large number of states existing next to it within a small energy range is subtle and is rather difficult to predict even by the state-of-the-art calculation techniques.

Moreover, the ground state is often severely influenced by perturbations like anisotropy or additional interactions to the simplest Heisenberg model. Furthermore to experiments, the presence of crystallographic disorder, which does exist more or less in actual compounds, tends to disturb and mask the intrinsic properties of frustrated systems.

## Dynamics of a Quantum Spin Liquid

Therefore, one has to be careful to enjoy the interesting frustration physics. In my presentation, I will focus on some frustrated spin systems from materials point of view. A particular emphasis will be on two kagome-type copper minerals: volborthite [1] and Cd-kapellasite CdK [2]. In addition, I would like to address our recent trials searching for novel magnets in 5 d transition metal compounds. Ishikawa, M. Yoshida, K. Nawa, M. Jeong, S. Berthier, M. Takigawa, M. Akaki, A. Miyake, M.

Tokunaga, K. Kindo, J. Yamaura, Y. Okamoto and Z. Hiroi, Phys. Okuma, T. Yajima, D. Nishio-Hamane, T. Okubo and Z. B 95, Vortex like spin arrangements called magnetic toroidal, magnetic monopole, and magnetic quadrupole moments are known as a source for unique symmetry-dependent phenomena such as linear magnetoelectric effects. We find that each Cu 4 O 12 spin cluster in these materials form a magnetic quadrupole type spin arrangement, which is stabilized due to the square cupola geometry.

We demonstrate that this ferroic magnetic quadrupole order gives rise to highly anistropic DC linear magnetoelectric effect, induction of electric polarization by an applied magnetic field. As an extension of the magnetoelectric effect into an optical regime, we also observe a nonreciprocal linear dichroism for visible light, i. These results indicate that the convex-shaped spin cluster can be a promising structural unit that hosts unique magnetoelectric responses arising from magnetic quadrupole moments.

Frustration is known to give rise to many interesting physical phenomena. One such example is magnetic fragmentation when original spins decompose into new elementary degrees of freedom. Inspired by Jospehson junctions arrays we propose a model of magnetic fragmentation on kagome lattice for classical planar spins with isotropic nearest-neighbor Heisenberg interactions and broken sublattice symmetry.

As couplings are varied, the groundstate exhibits a transition from plain ferromagnet to a highly degenerate manifold of states that retain non-zero magnetisation. Importantly this behavior, i. We analyse the properties of these groundstates, like correlations and long-wavelength behaviour. Finally we discuss how this model can be extended to different types of spins and other 2D and 3D lattices. An impurity in a Tomonaga-Luttinger liquid leads to a crossover between short- and long-distance regime which describes many physical phenomena. However, calculation of the entire crossover of correlation functions over different length scales has been difficult.

We develop a powerful numerical method based on infinite DMRG. By utilizing infinite boundary conditions we can obtain correlation functions within a finite-size window that contains the impurity. The effects of quantum fluctuations in the Heisenberg model on the isotropic and breathing pyrochlore lattices are discussed for a generic spin-S.

The effects of temperature, quantum fluctuations, breathing anisotropies, and further neighbor Heisenberg couplings, on the nature of the scattering profile, and the pinch points in particular, are analyzed. Reference: arXiv: Iqbal, T. Ghosh, M. Gingras, H. Jeschke, S. Rachel, J.

### Bibliographic Information

Reuther, and R. Thomale We show that the tunneling conductance G of such a junction becomes independent of the barrier strength in the thin barrier limit. We show that this independence is a consequence of the change in the topological winding number of the Weyl nodes across the junction and point out that it has no analogue in tunneling conductance of either junctions of two-dimensional topological materials such as graphene or topological insulators or those made out of Weyl or multi-Weyl semimetals with same topological winding numbers.

We study this phenomenon both for normal-barrier-normal NBN and normal-barrier-superconducting NBS junctions involving Weyl and multi-Weyl semimetals and discuss experiments which can test our theory. Weak Mott insulators emerge from 5d electron systems with strong spin-orbit interactions. Coulomb repulsion U between electrons in 5d orbitals is not strong enough to suppress charge degrees of freedom completely. For example, the charge gap is comparable to the magnon-band width for strontium iridates. Such electron systems can be described by the Hubbard model with an intermediate U, which would be in the crossover regime between Slater and Mott insulators.

Reliable calculation for the intermediate-U region is theoretically challenging because of the lack of a small parameter in the model. We have developed a new numerical approach that enables efficient calculation of dynamical quantities at finite temperatures in the broad-U region. The sampling of auxiliary vector fields from the Boltzmann distribution and the real time dynamics of the density matrix are successfully combined in our method.