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The entanglement spectrum (ES) has been a successful tool for the exploration of (2+1)-dimensional chiral topological states, through Li and Haldane's method of counting degeneracies in the low-lying ES characteristic of an underlying conformal field theory (CFT) [H. Li and F. D. M. Haldane, Phys. Rev. Lett. 101, 010504 (2008)]. We develop an quantitative understanding of the splitting of these degeneracies in the real space ES, at fixed momentum, that occurs at finite size, based on a Generalized Gibbs Ensemble (GGE) of local conservation laws that arise directly from, and are thus controlled by, the chiral CFT. These conservation laws come from viewing the conformal boundary state description of the ES as a quantum quench. We apply this by computing such conservation laws for chiral SU(2)-level-one and -level-two, and later chiral SU(3)-level-one, Wess-Zumino-Witten CFTs, and successfully matching these with numerically calculated entanglement spectra for corresponding chiral spin liquid states, including PEPS. For the chiral SU(2)-level-two case, we find that essential to the GGE are local integrals of operators of fractional dimension, as proposed by Cardy in [J. Stat. Mech.: Theory Exp. 2016 (2), 023103] for quantum quenches. One such operator, G(x), has lower conformal dimension than the energy-momentum tensor, T(x), and we discuss possible consequences of this. Meanwhile in the chiral SU(3)-level-one case, we find that integrals of odd-dimensional operators are available from the CFT, which are the only ones that can be responsible for breaking the degeneracy of SU(3) conjugates, but they are excluded from the GGE by discrete symmetries, for a chiral state. This prediction of conjugate degeneracy in the chiral SU(3)-level-one spin liquid state is backed by the numerical ES to which we match our chiral SU(3)-level-one ensemble of conservation laws.Along the way, we develop a "doubled" SU(3)-level-one theory to fully explain the low-lying entanglement spectrum of an SU(3) spin liquid PEPS [I. Kurečić, L. Vanderstraeten, and N. Schuch, Phys. Rev. B 99, 045116 (2019)] that strongly breaks time-reversal symmetry and possesses chiral SU(3)-level-one Li-Haldane counting in some ES sectors, but not others. This clarifies the non-chirality of that state. We then use the PEPS's sectors which exhibit Li-Haldane state counting of a chiral state, but which do exhibit breaking of the degeneracy of SU(3) conjugates, to exhibit a clear contrast with the chiral SU(3)-level-one spin liquid state we previously examined, and demonstrate the utility of broken conjugate degeneracy as a diagnostic of the absence of chirality.

Transition metal compounds have long been known to host intriguing many-body ground states owing to a fine interplay between electron-electron interactions, electron-phonon coupling, and low dimensionality. Recent advances in van der Waals synthesis have enabled the experimental studies of transition metal dichalcogenides in the extreme two-dimensional limit. In this dissertation I will discuss experiments that probe novel many-body ground states in single-layer transition metal dichalcogenides via the use of scanning tunneling microscopy and spectroscopy (STM/STS). The first part of the dissertation focuses on charge density wave states in single-layer 1H-NbSe2, single-layer 1H-TaSe2, and single-layer 1T-TaSe2 and the mechanisms by which they arise. The second part of the dissertation discusses an exotic Mott insulator electronic ground state in single-layer 1T-TaSe2 and its collapse with increased temperature and/or the introduction of interlayer coupling. In the third part of the dissertation I present evidence supporting a novel many-body magnetic ground state called a quantum spin liquid in the spin channel of single-layer 1T-TaSe2. This gapless spin liquid state was probed by spectroscopic STM imaging as well as by its response to single magnetic impurities. The results discussed here establish new platforms for investigating correlation physics in two dimensions and provide insights into the intriguing many-body phases therein.

Charge doping to Mott insulators is critical to realize high-temperature superconductivity, quantum spin liquid state, and Majorana fermion, which would contribute to quantum computation. Mott insulators also have a great potential for optoelectronic applications; however, they showed insufficient photoresponse in previous reports. To enhance the photoresponse of Mott insulators, charge doping is a promising strategy since it leads to effective modification of electronic structure near the Fermi level. Intercalation, which is the ion insertion into the van der Waals gap of layered materials, is an effective charge-doping method without defect generation. Herein, we showed significant enhancement of optoelectronic properties of a layered Mott insulator, α-RuCl3, through electron doping by organic cation intercalation. The electron-doping results in substantial electronic structure change, leading to the bandgap shrinkage from 1.2 eV to 0.7 eV. Due to localized excessive electrons in RuCl3, distinct density of states is generated in the valence band, leading to the optical absorption change rather than metallic transition even in substantial doping concentration. The stable near-infrared photodetector using electronic modulated RuCl3 showed 50 times higher photoresponsivity and 3 times faster response time compared to those of pristine RuCl3, which contributes to overcoming the disadvantage of a Mott insulator as a promising optoelectronic device and expanding the material libraries.

The identification of low-energy thermal excitations in SmMnO3+δ degenerate states of spin and superconducting quantum liquids in magnetic fields H ≤ 3.5 kOe is presented. In the temperature interval 4.2–12 K, the Landau quantization of the low-energy magnetic excitations pair spectrum of Z2 quantum spin liquid is found in the system spinon-gauge field. The formation of a broad continuum of spinon pair excitations in the “weak magnetic field” regime (H = 100 Oe, 1 kOe) in the FC regime is explained in the framework of the Landau quantization models of the compressible spinon gas with fractional values of the factor ν filling three overlapping bands. In the regime of “strong magnetic field” (H = 3.5 kOe), the quantum oscillations of temperature dependences of “supermagnetization” of the incompressible spinon liquid were observed. They have the form of three narrow steps (plateaus), corresponding to a complete filling of the non-overlapping Landau bands with integer values of the filling factor by spinons. These results are evidence for the existence of vortex gauge field fluctuations with a high density in the magnetic fields H ≥ 100 Oe. The strong growth of vortex fluctuations can be explained by a second-kind phase transition in SmMnO3+δ in the form of the vortices condensation. Growth of the external dc magnetic field strength in the SmMnO3+δ samples in the interval of fields 0

In this work, we studied the magnetic properties of a regularly tetrahedral molecule made of four spin-½, interconnected by exchange. For this purpose, we used the Heisenberg model and performed an exact resolution. In the case of a ferromagnetic coupling among the spins, the system orders itself under a magnetic field without displaying any net spontaneous magnetization. It behaves as a high spin-2 unique magnet. Under antiferromagnetic exchange, some exotic behaviour has been revealed due to the frustration governing the spin edifice. Thus, the magnetization is quantized into plateaus, which are separated by quantum phase transitions. In particular, we have argued the possibility of a quantum spin liquid (QSL) state that can occur at low temperature. This contribution intends mainly to bring single-molecular magnets to the front line of innovative nanoscale applications.

In recent years, several magnetic Mott insulators with strong spin-orbit coupling were suggested to be proximate to the Kitaev quantum spin liquid, whose one of the most exciting features is the fractionalization of spin excitations into itinerant Majorana fermions and static Z2 fluxes. Unfortunately, the ground states of these systems cannot be easily captured by experiment, remaining featureless to conventional local probes. Here, we propose to study the signatures of fractionalized excitations by exploiting their coupling to the lattice vibrations, dubbed magnetoelastic coupling, which arises from the fact that the interaction between spins depends on the relative distance between them. We argue that the magnetoelastic coupling can lead to the distinct modification of the phonon dynamics, which can be observed by measuring renormalized phonon spectrum, the sound attenuation, and the phonon Hall viscosity. This makes the phonon dynamics a promising tool for the characterization and identification of quantum spin liquid phases. In this work, we focus on the magnetoelastic effects in the three-dimensional Kitaev model realized on the hyperhoneycomb lattice. The hyperhoneycomb Kitaev spin liquid is particularly interesting since the strong Kitaev interaction was observed in the Kitaev magnet β-Li2IrO3, for which the spin-orbit entangled Jeff = 1/2 moments of iridium ions form precisely the hyperhoneycomb lattice.

The pyrochlore lattice is associated with several potential and actual spin liquid phases as a result of its strong geometric frustration. At finite temperature, these can exhibit an unusually broad cross-over regime to a conventional paramagnet. Here, we study this regime analytically by showing how a single-tetrahedron Hamiltonian can extrapolate beyond the first term of a high-temperature expansion and yield insights into the build-up of correlations. We discuss how this unusual behaviour is brought about by the structure of the eigenspaces of the coupling matrix. Further interesting behaviour can appear for parameter values located near phase transitions: we find coexistence of $(111)$ rods and $(220)$ peaks in the structure factor, as observed in neutron scattering experiments on Yb$_2$Ti$_2$O$_7$., Comment: 7 pages, 4 figures

Two-dimensional triangular-lattice antiferromagnets are predicted under some conditions to exhibit a quantum spin liquid ground state with no energy barrier to create emergent, fractionalized spinon excitations that carry spin but no charge. Materials that realize this kind of spin liquid are expected to have a low-energy behaviour described by a spinon Fermi surface. Directly imaging the resulting spinons, however, is difficult due to their chargeless nature. Here we use scanning tunnelling spectroscopy to image density waves consistent with the predictions of spinon density modulation arising from a spinon Fermi surface instability in single-layer 1T-TaSe2. We confirm the existence of a triangular lattice of localized spins in this material by contacting it with a metallic 1H-TaSe2 substrate and measuring the Kondo effect. Spectroscopic imaging of isolated single-layer 1T-TaSe2 reveals long-wavelength super-modulations at Hubbard band energies, consistent with the predicted behaviour of itinerant spinons. These super-modulations allow the direct experimental measurement of the spinon Fermi wavevector, in good agreement with theoretical predictions for a two-dimensional quantum spin liquid. Some quantum spin liquids are expected to have an effective Fermi surface of fractionalized spinon excitations. The two-dimensional spin liquid candidate 1T-TaSe2 has charge density modulations that may be caused by an unstable spinon Fermi surface.

A family of spin-orbit coupled honeycomb Mott insulators offers a playground to search for quantum spin liquids (QSLs) via bond-dependent interactions. In candidate materials, a symmetric off-diagonal $\Gamma$ term, close cousin of Kitaev interaction, has emerged as another source of frustration that is essential for complete understanding of these systems. However, the ground state of honeycomb $\Gamma$ model remains elusive, with a suggested zigzag magnetic order. Here we attempt to resolve the puzzle by perturbing the $\Gamma$ region with a staggered Heisenberg interaction which favours the zigzag ordering. Despite such favour, we find a wide disordered region inclusive of the $\Gamma$ limit in the phase diagram. Further, this phase exhibits a vanishing energy gap, a collapse of excitation spectrum, and a logarithmic entanglement entropy scaling on long cylinders, indicating a gapless QSL. Other quantities such as plaquette-plaquette correlation are also discussed., Comment: 11+16 pages. npj Quantum Materials (in press). Typos (e.g., central charge) are fixed. Some additional results and references will be considered in future

The Kitaev quantum spin liquid epitomizes an entangled topological state, for which two flavors of fractionalized low-energy excitations are predicted: the itinerant Majorana fermion and the Z2 gauge flux. It was proposed recently that fingerprints of fractional excitations are encoded in the phonon spectra of Kitaev quantum spin liquids through a novel fractional-excitation-phonon coupling. Here, we detect anomalous phonon effects in α-RuCl3 using inelastic X-ray scattering with meV resolution. At high temperature, we discover interlaced optical phonons intercepting a transverse acoustic phonon between 3 and 7 meV. Upon decreasing temperature, the optical phonons display a large intensity enhancement near the Kitaev energy, JK~8 meV, that coincides with a giant acoustic phonon softening near the Z2 gauge flux energy scale. These phonon anomalies signify the coupling of phonon and Kitaev magnetic excitations in α-RuCl3 and demonstrates a proof-of-principle method to detect anomalous excitations in topological quantum materials. It was recently proposed that the coupling between phonons and fractional excitations of a Kitaev quantum spin liquid can be detected in its phonon dynamics. Here, the authors report signatures of this coupling, manifested in low-energy phonon anomalies measured by inelastic X-ray scattering with meV resolution.

The frustrated magnet $\alpha$-RuCl$_3$ constitutes a fascinating quantum material platform that harbors the intriguing Kitaev physics. However, a consensus on its intricate spin interactions and field-induced quantum phases has not been reached yet. Here we exploit multiple state-of-the-art many-body methods and determine the microscopic spin model that quantitatively explains major observations in $\alpha$-RuCl$_3$, including the zigzag order, double-peak specific heat, magnetic anisotropy, and the characteristic M-star dynamical spin structure, etc. According to our model simulations, the in-plane field drives the system into the polarized phase at about 7 T and a thermal fractionalization occurs at finite temperature, reconciling observations in different experiments. Under out-of-plane fields, the zigzag order is suppressed at 35 T, above which, and below a polarization field of 100 T level, there emerges a field-induced quantum spin liquid. The fractional entropy and algebraic low-temperature specific heat unveil the nature of a gapless spin liquid, which can be explored in high-field measurements on $\alpha$-RuCl$_3$., Comment: To appear in Nature Communications (12 pages, 6 figures, and 5 Supplementary Notes)

In the class of materials called spin liquids1–3, a magnetically ordered state cannot be attained even at millikelvin temperatures because of conflicting constraints on each spin; for example, from geometric or exchange frustration. The resulting quantum spin-liquid state is currently of intense interest because it exhibits unusual excitations as well as wave-function entanglement. The layered insulator α-RuCl3 orders as a zigzag antiferromagnet at low temperature in zero magnetic field4. The zigzag order is destroyed when a magnetic field is applied parallel to the zigzag axis. At moderate magnetic field strength, there is growing evidence that a quantum spin-liquid state exists. Here we report the observation of oscillations in its thermal conductivity in that field range. The oscillations, whose amplitude is very large within this field range and strongly suppressed on either side, are periodic. This is analogous to quantum oscillations in metals, even though α-RuCl3 is an excellent insulator with a large gap. As the temperature is raised above 0.5 K, the oscillation amplitude decreases exponentially, anticorrelating with the emergence of an anomalous planar thermal Hall conductivity above approximately 2 K. Transport measurements on the Kitaev quantum spin liquid candidate α-RuCl3 subjected to a magnetic field reveal oscillating behaviour in its thermal conductivity, reminiscent of Shubnikov de Haas oscillations in metals.

Geometrical frustration, quantum entanglement and disorder may prevent long-range order of localized spins with strong exchange interactions, resulting in a novel state of matter. $\kappa$-(BEDT-TTF)$_2$-Cu$_2$(CN)$_3$ is considered the best approximation of this elusive quantum-spin-liquid state, but its ground-state properties remain puzzling. Here we present a multi-frequency electron-spin resonance study down to millikelvin temperatures, revealing a rapid drop of the spin susceptibility at $T^*=6\,\mathrm{K}$. This opening of a spin gap, accompanied by structural modifications, suggests the enigmatic `$6\,\mathrm{K}$-anomaly' as the transition to a valence-bond-solid ground state. We identify an impurity contribution that becomes dominant when the intrinsic spins form singlets. Only probing the electrons directly manifests the pivotal role of defects for the low-energy properties of quantum-spin systems without magnetic order., Comment: 34 pages, 17 figures

Realization of the Kagome antiferromagnetic (KAF) lattice is of high interest because the geometric frustration in the Kagome lattice is expected to give rise to highly degenerated ground states that may host exotic phases such as quantum spin liquid. Here we demonstrate the design and synthesis of a single-layer two-dimensional metal-organic framework (2D-MOF) containing a Kagome lattice of Fe(II) ions assembled on a Au(111) surface. First-principles calculations reveal that the Fe(II) ions are at a high spin state of S = 2 and are coupled antiferromagnetically with nearest-neighboring exchange J1 = 5.8 meV. The ground state comprises various degenerated spin configurations including the well-known q = 0 and q = √3 × √3 phases. Remarkably, we observe a spin excitation at 6 meV using tunneling spectroscopy. This work points out a feasible route toward realizing spin 1/2 KAF, a candidate quantum spin liquid system, by replacing Fe(II) by Cu(II) in the same structure.

Complex iridium oxides have attracted recently a substantial interdisciplinary attention due to an intimate entanglement of spin and orbital degrees of freedom which may give rise to a novel spin–orbital Mott insulating behavior and exotic quantum spin liquid phases. Electron spin resonance (ESR) spectroscopy is known to be an instructive tool for studying the spin–orbital coupling (SOC) effects as it can directly access the relevant parameters sensitive to SOC, such as the g factor tensor, magnetic anisotropy gaps and spin dynamics. In this article, a systematic study at the Leibniz IFW Dresden of the static and dynamic properties of selected Ir-based materials with multi-frequency high-field ESR spectroscopy will be reviewed. Specifically, evidence for a surprisingly isotropic antiferromagnetic spin dynamics and the inversion of the orbital states in the prototypical spin–orbital Mott insulator $$\text {Sr}_2\text {IrO}_4$$ Sr 2 IrO 4 , observation of the collective resonance modes in the family of double perovskites $$\text {La}_2$$ La 2 B$$\text {IrO}_6$$ IrO 6 (B = Cu, Co) and the origin of the unexpected magnetism in the double perovskite $$\text {Ba}_2\text {YIrO}_6$$ Ba 2 YIrO 6 will be highlighted.

The electronic properties of molecular conductors can be readily varied via physical or chemical pressure as it enlarges the bandwidth W. This enables them to cross the Mott insulator-to-metal phase transition by reducing electronic correlations U/W. Here we introduce an alternative path by spatially expanding the molecular orbitals when partially replacing sulfur by selenium in the constituting bis-(ethylenedithio)-tetrathiafulvalene (BEDT-TTF) molecules of the title compound. We characterize how the insulating quantum-spin-liquid state is tuned via a Mott transition to the metallic Fermi-liquid state crossing a narrow region of superconductivity. The transport, dielectric, and optical measurements reveal that at this first-order phase transition, metallic regions coexist in the insulating matrix leading to pronounced percolative effects, which are most obvious in the strong enhancement of the dielectric constant at low temperatures.

The Cu(II) ions in [(C2H5)3NH]2Cu2(C2O4)3 form a hyperhoneycomb lattice and show no indication of long-range magnetic order down to 60 mK. It has therefore been suggested that [(C2H5)3NH]2Cu2(C2O4)3 is a three dimensional quantum spin liquid. We construct a tight-binding model of [(C2H5)3NH]2Cu2(C2O4)3 from Wannier orbital overlaps. Including interactions within the Jahn–Teller distorted Cu-centered eg Wannier orbitals leads to a highly anisotropic effective Heisenberg model. We show that this anisotropy arrises from interference between different superexchange pathways. This demonstrates that when two (or more) orbitals contribute to the localised spin superexchange can be significantly richer than in the textbook single orbital case. The hyper-honeycomb lattice contains two symmetry distinct sublattices of Cu atoms arranged in coupled chains. We show that one sublattice is strongly dimerized, the other forms isotropic antiferromagnetic chains. Integrating out the strongest (intradimer) exchange interactions leaves extremely weakly coupled Heisenberg chains.

In 1983, F. Duncan M. Haldane predicted a singlet ground state for isolated integer-spin one-dimensional antiferromagnets with low single-ion anisotropy D. Since then, a lot of species containing c...

We review terahertz (THz) electron spin resonance studies of two types of exotic quantum spin systems, namely, the spin(S)-1/2 one-dimensional (1D) Ising-like antiferromagnet BaCo $$_2$$ V $$_2$$ O $$_8$$ and the S=1/2 two-dimensional (2D) honeycomb-like antiferromagnet Ba $$_3$$ CuSb $$_2$$ O $$_9$$ in magnetic fields of up to 50 T. For the former subject, unconventional magnetic excitations were identified below a critical magnetic field $$H_c$$ ( $$\sim $$ 4 T), where the exotic field-induced order-to-disorder transition occurs, and magnetic excitations in a Tomonaga-Luttinger liquid state were observed above $$H_c$$ . The novel magnetic excitations were analyzed with an S=1/2 1D XXZ model by considering the peculiar structure of this compound. For the latter subject, the orbital quantum dynamics of the spin liquid candidate Ba $$_3$$ CuSb $$_2$$ O $$_9$$ was revealed using multifrequency electron spin resonance ranging from 9.3 GHz to 0.73 THz. The g-factor of the hexagonal Ba $$_3$$ CuSb $$_2$$ O $$_9$$ single crystal possesses a weak six-fold symmetry at low frequencies, while two-fold symmetry is manifested at high frequencies. From the critical point between the two frequency regions, the frequency of the dynamic Jahn-Teller distortion is determined to be approximately 10 GHz. This dynamic distortion, accompanied by orbital quantum tunneling, proves the spin-orbital liquid state in Ba $$_3$$ CuSb $$_2$$ O $$_9$$ .

We report the observation of metal-like to insulator transition (MTI) in the 3d pyrochlore oxide Tb2Ti2O7 at 603 K due to the interaction of empty 3d orbitals of Ti4+ with O2– ions, evidenced by th...

The bond-disordered Kitaev model attracts much attention due to the experimental relevance in $\alpha$-RuCl$_3$ and $A_3$LiIr$_2$O$_6$ ($A=$ H, D, Ag, $\textit{etc.}$). Applying a magnetic field to break the time-reversal symmetry leads to a strong modulation in mass terms for Dirac cones. Because of the smallness of the flux gap of the Kitaev model, a small bond disorder can have large influence on itinerant Majorana fermions, and Majorana fermions will be in the Anderson localization state immediately. We call this immobile liquid state Anderson-Kitaev liquid state with two localized Majorana fermions, one frozen by gauge fluctuations and the other localized by disordered mass terms. The quantization of the thermal Hall conductivity $\kappa/T$ disappears by a quantum Hall transition induced by a small disorder, and $\kappa/T$ shows a rapid crossover into the Anderson-Kitaev liquid with a negligible Hall current. Especially, the critical disorder strength $\delta J_{c1} \sim 0.05$ in the unit of the Kitaev interaction would have many implications for the stability of Kitaev spin liquids., Comment: 6+4 pages, 3+2 figures. This is a preprint of an article published in npj Quantum Mater. The final authenticated version is available online at: https://doi.org/10.1038/s41535-020-00285-3

In RuCl$_3$, inelastic neutron scattering and Raman spectroscopy reveal a continuum of non-spin-wave excitations that persists to high temperature, suggesting the presence of a spin liquid state on a honeycomb lattice. In the context of the Kitaev model, magnetic fields introduce finite interactions between the elementary excitations, and thus the effects of high magnetic fields - comparable to the spin exchange energy scale - must be explored. Here we report measurements of the magnetotropic coefficient - the second derivative of the free energy with respect to magnetic field orientation - over a wide range of magnetic fields and temperatures. We find that magnetic field and temperature compete to determine the magnetic response in a way that is independent of the large intrinsic exchange interaction energy. This emergent scale-invariant magnetic anisotropy provides evidence for a high degree of exchange frustration that favors the formation of a spin liquid state in RuCl$_3$., Comment: arXiv admin note: substantial text overlap with arXiv:1901.09245. Nature Physics

S = 1/2 kagome-lattice hydroxychlorides are promising candidates for realizing the elusive quantum spin liquid (QSL) state. Herbertsmithite [Cu3Zn(OH)6Cl2], a naturally occurring hydroxychloride mi...

1T-TaS$_2$ undergoes successive phase transitions upon cooling and eventually enters an insulating state of mysterious origin. Some consider this state to be a band insulator with interlayer stacking order, yet others attribute it to Mott physics that support a quantum spin liquid state.Here, we determine the electronic and structural properties of 1T-TaS$_2$ using angle-resolved photoemission spectroscopy and X-Ray diffraction. At low temperatures, the 2$\pi$/2c-periodic band dispersion, along with half-integer-indexed diffraction peaks along the c axis, unambiguously indicates that the ground state of 1T-TaS$_2$ is a band insulator with interlayer dimerization. Upon heating, however, the system undergoes a transition into a Mott insulating state, which only exists in a narrow temperature window. Our results refute the idea of searching for quantum magnetism in 1T-TaS$_2$ only at low temperatures, and highlight the competition between on-site Coulomb repulsion and interlayer hopping as a crucial aspect for understanding the material's electronic properties., Comment: 5 figures, Supplementary information

Significance In “Planckian metals,” electrons dissipate energy at the fastest possible rate allowed by the fundamental laws of quantum mechanics, resulting in a linear temperature dependence of their electrical resistivity. Although observed for a number of quantum materials, this phenomenon lacks a general theoretical understanding and is often considered as one of the prominent fundamental questions in condensed matter physics. Here, we show that Planckian dissipation and a behavior consistent with the “marginal Fermi liquid” phenomenology emerge in the quantum critical regime separating a Mott insulating spin glass and a Fermi liquid. By establishing this behavior in an explicit model solvable by state-of-the-art computational methods, our theory paves the way toward a deeper understanding of Planckian or “strange” metals., “Strange metals” with resistivity depending linearly on temperature T down to low T have been a long-standing puzzle in condensed matter physics. Here, we consider a lattice model of itinerant spin-1/2 fermions interacting via onsite Hubbard interaction and random infinite-ranged spin–spin interaction. We show that the quantum critical point associated with the melting of the spin-glass phase by charge fluctuations displays non-Fermi liquid behavior, with local spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This extends the quantum spin liquid dynamics previously established in the large-M limit of SU(M) symmetric models to models with physical SU(2) spin-1/2 electrons. Remarkably, the quantum critical regime also features a Planckian linear-T resistivity associated with a T-linear scattering rate and a frequency dependence of the electronic self-energy consistent with the marginal Fermi liquid phenomenology.

Observation of a quantum spin liquid (QSL) state is one of the most important goals in condensed-matter physics, as well as the development of new spintronic devices that support next-generation industries. The QSL in two dimensional quantum spin systems is expected to be due to geometrical magnetic frustration, and thus a kagome-based lattice is the most probable playground for QSL. Here, we report the first experimental results of the QSL state on a square-kagome quantum antiferromagnet, KCu6AlBiO4(SO4)5Cl. Comprehensive experimental studies via magnetic susceptibility, magnetisation, heat capacity, muon spin relaxation (μSR), and inelastic neutron scattering (INS) measurements reveal the formation of a gapless QSL at very low temperatures close to the ground state. The QSL behavior cannot be explained fully by a frustrated Heisenberg model with nearest-neighbor exchange interactions, providing a theoretical challenge to unveil the nature of the QSL state., There exist many theoretical models of frustrated quantum magnetism, most of which lack convincing experimental realisations. Here the authors combine several experimental methods to argue that KCu6AlBiO4(SO4)5Cl behaves as a square-kagome-lattice quantum Heisenberg antiferromagnet.

Some magnets due to particular geometry of the exchange bonds do not undergo transition to the conventional magnetically ordered state despite of the presence of significant exchange couplings. Instead, a collective paramagnetic state is formed. The later state can remain stable down to $T=0$ if the ground state of this magnet turns out to be nonmagnetic singlet separated from the excited triplet states by an energy gap. Low-temperature spin dynamics of the collective paramagnets with gapped excitations spectrum (or spin-gap magnets) can be described in terms of a dilute gas of the triplet excitations. Applied magnetic field can suppress the energy gap, resulting in the formation of the gapless spin-liquid state or even leading to the unusual phenomenon of field-induced antiferromagnetic order. Introduction of defects in the crystallographic structure of the spin-gap magnet can result either in the formation of multi-spin paramagnetic center or in the formation of randomly distributed modified exchange bonds in the crystal. This review includes results of electron spin resonance (ESR) spectroscopy study of several representative quantum paramagnets with gapped excitations spectrum: quasy-two-dimensional magnet \phcc{}, quasy-one-dimensional magnets of "spin-tube" type \sul{} and "spin-ladder" type \dimpy{}. We will demonstrate that ESR absorption spectra reveal common features of these systems: ESR spectroscopy allows to observe and characterize fine structure if the triplet energy levels, to identify many-particles relaxation processes in the gas of triplet excitations and to observe collective spin-wave oscillations in the field induced antiferromagnetically ordered state, as well as to observe some individual features of the studied systems., Comment: This text is an expanded author-translated version of the review prepared for the memorial issue of Journal of Experimental and Theoretical Physics dedicated to 100-year anniversary of A.S.~Borovik-Romanov (full memorial volume is available as JETP 131 No.1 (2020) [ZhETF 158 No.1 (2020)])

Among the vast pyrochlore group, oxide bismuth pyrochlores are quite interesting owing to the presence of stereochemically active lone pair electrons of bismuth and prominent Jahn-Teller interactions of the pyrochlore constituent cations leading to interesting structural modifications as well as emerging physical phenomenon of fundamental and technological significance. Particularly the bismuth pyrochlores nominally denoted by (Bi,M)MNO7-δ (M = transition metal, N= Nb, Ta, Sb) crystallizing with cubic symmetry at ambient conditions are intriguing due to the presence of ionic displacements and mixed cation occupancy especially at Bi site leading to non-stoichiometry and tunability of the physical properties with composition. Magnetic properties of the pyrochlore lattice has also garnered much attention as spin polarization on the frustrated square lattice indicated distinctive magnetic ground states such as spin glass, spin ice and spin liquid. In these cubic pyrochlores large cationic displacements coupled with uncontrolled random hopping, mixed cation crystallographic site occupancy and compositional variability gave rise to tunable dielectric relaxation. The cubic pyrochlore have been well known for showing low temperature as well as high temperature dielectric relaxation. Although long-range magnetic order was not supported on a bismuth pyrochlore lattice, recent findings reflected polar nature at room temperature in some of these disordered cubic pyrochlores comprising of highly polarizable cations. Herein we summarize the state of art in the exploration of cubic pyrochlores of Bi, and Nb/Ta/Sb in combination with various transition metals occupying multiple crystallographic sites. Their interesting structural, dielectric, magnetic properties and device applications are highlighted. Current challenges in the understanding of these materials are discussed and conclusions are put forth.

Conventional phase transitions are well understood in terms of the order parameter, based on the Landau–Ginzburg–Wilson theory. However, unconventional magnetic orders have been observed in clean systems such as MnSi. The unconventional magnetic orders of conduction electrons in the metallic phase has been observed for high-temperature superconductors and heavy fermion compounds. However, these unconventional magnetic orders have been limited to relatively low temperatures as quantum phase transitions. Here high-temperature magnetic short-range order is observed as one of the unconventional magnetic orders at temperatures up to 720 K in a noncentrosymmetric intermetallic antiferromagnet Mn3RhSi with a well-ordered lattice. The magnetic Mn ions form a hyperkagome network of corner-sharing triangles, where the spins are geometrically frustrated. The spin network is equivalent to that of a spin liquid and non-Fermi-liquid material, β-Mn. Our observation indicates that a metallic phase with magnetic short-range order exists at high temperatures. Magnetic short-range ordering has been observed at low temperatures as quantum phase transitions in some compounds. Here, magnetic short-range ordering is found to remain at temperatures up to 720 K in noncentrosymmetric Mn3RhSi.

$\alpha$-RuCl$_3$ is drawing much attention as a promising candidate Kitaev quantum spin liquid. However, despite intensive research efforts, controversy remains about the form of the basic interactions governing the physics of this material. Even the sign of the Kitaev interaction (the bond-dependent anisotropic interaction responsible for Kitaev physics) is still under debate, with conflicting results from theoretical and experimental studies. The significance of the symmetric off-diagonal exchange interaction (referred to as the $\Gamma$ term) is another contentious question. Here, we present resonant elastic x-ray scattering data that provides unambiguous experimental constraints to the two leading terms in the magnetic interaction Hamiltonian. We show that the Kitaev interaction ($K$) is ferromagnetic, and that the $\Gamma$ term is antiferromagnetic and comparable in size to the Kitaev interaction. Our findings also provide a natural explanation for the large anisotropy of the magnetic susceptibility in $\alpha$-RuCl$_3$ as arising from the large $\Gamma$ term. We therefore provide a crucial foundation for understanding the interactions underpinning the exotic magnetic behaviours observed in $\alpha$-RuCl$_3$., Comment: 5 pages, two-column, 3 figures

Materials with two-dimensional, geometrically frustrated, spin-1/2 lattices provide a fertile playground for the study of intriguing magnetic phenomena such as quantum spin liquid (QSL) behavior, b...

The ground-state of S = 1 kagome lattice antiferromagnets (KLAFs), in the presence of strong geometric frustration and the smallest integer spin, has the potential to host a range of non-trivial magnetic phases including a quantum spin liquid. The effect of local geometry and metal-ion electronic structure on the formation of these predicted phases remain unknown due to, in part, the lack of an ideal analyte. Herein, a kagome lattice compound, (CH3NH3)2NaV3F12 (1-V), featuring a single distinct V3+ (d2) site in the Rm space group, was synthesized hydrothermally. In this S = 1, d2 system, the trivalent vanadium ions are tetragonally compressed due to Jahn–Teller distortion. The interlayer methylammonium cations show static positional disorder with three possible orientations. The negative Curie–Weiss temperature and dominant antiferromagnetic interactions make 1-V a candidate to study S = 1 KLAF physics. The frequency-dependence of ac magnetic susceptibility and the heat capacity results suggest that 1-V has a spin glass ground state. This freezing of the spin dynamics may be due to competing exchange interactions, structural imperfection arising from the static disorder of the interlayer methylammonium cations or the presence of ‘defect’-like spins.

The kagome Heisenberg antiferromagnet formed by frustrated spins arranged in a lattice of corner-sharing triangles is a prime candidate for hosting a quantum spin liquid (QSL) ground state consisting of entangled spin singlets. But the existence of various competing states makes a convincing theoretical prediction of the QSL ground state difficult, calling for experimental clues from model materials. The kagome lattice materials Zn-barlowite ZnCu$_{3}$(OD)$_{6}$FBr and herbertsmithite ZnCu$_{3}$(OD)$_{6}$Cl$_2$ do not exhibit long range order, and they are considered the best realizations of the kagome Heisenberg antiferromagnet known to date. Here we use $^{63}$Cu nuclear quadrupole resonance combined with the inverse Laplace transform (ILT) to probe locally the inhomogeneity of delicate quantum ground states affected by disorder. We present direct evidence for the gradual emergence of spin singlets with spatially varying excitation gaps, but even at temperatures far below the super-exchange energy scale their fraction is limited to approximately 60\% of the total spins. Theoretical models need to incorporate the role of disorder to account for the observed inhomogeneously gapped behaviour., Comment: 4 Figs

We present a large-scale density matrix renormalization group (DMRG) study of the spin-$1$ SU(3) bilinear-biquadratic model on the square lattice, which was suggested to host a nematic spin liquid state in recent DMRG calculations. We report that this spin liquid appears to strongly compete with a three-sublattice magnetic order. To further study the competition between the two states, and the reason of the emergent nematic spin liquid, we included an additional next-nearest-neighbor SU(3) symmetric interactions along one of the two plaquette diagonal directions. This allows to tune the square-lattice model to the triangular-lattice model. By computing spin correlation functions and various order parameters, we find that the three-sublattice order may develop at infinitesimal additional new coupling, at least within the precision of our study. Compared with the previous findings that the nematic spin liquid is stable in extended parameter regions with additional couplings that respect the lattice symmetries of the square lattice, we argue that here the diagonal couplings, which frustrate the bipartite-lattice structure, rapidly suppress the two-sublattice fluctuations and the three-sublattice order thus wins. This numerical result is consistent with the conjecture that the nematic spin liquid emerges from the competition between two- and three-sublattice fluctuations., 7 pages, 7 figures

Long-range entanglement in quantum spin liquids (QSLs) leads to novel low-energy excitations with fractionalized quantum numbers and (in two dimensions) statistics. Experimental detection and manipulation of these excitations present a challenge particularly in view of diverse candidate magnets. A promising probe of fractionalization is their coupling to phonons. Here, we present Raman scattering results for the $S=1/2$ honeycomb iridate ${\mathrm{Cu}}_{2}{\mathrm{IrO}}_{3}$, a candidate Kitaev QSL with fractionalized Majorana fermions and Ising flux excitations. We observe anomalous low-temperature frequency shift and linewidth broadening of the Raman intensities in addition to a broad magnetic continuum, both of which, as we derive, are naturally attributed to the phonon decaying into itinerant Majoranas. The dynamic Raman susceptibility marks a crossover from the QSL to a thermal paramagnet at $\ensuremath{\sim}120$ K. The phonon anomalies below this temperature demonstrate a strong phonon-Majorana coupling. These results provide evidence of spin fractionalization in ${\mathrm{Cu}}_{2}{\mathrm{IrO}}_{3}$.