The physical properties of rare-earth (RE) dodecaborides, characterized by a cage-glass crystal structure with loosely bound RE ions, are reviewed. These compounds are strongly correlated electron systems with simultaneously active charge, spin, orbital, and lattice degrees of freedom, which explains the complexity of all $R\mathrm{B}_{12}$ compounds including antiferromagnetic (TbB$_{12}$-TmB$_{12}$) and nonmagnetic (LuB$_{12}$) metals, on one side, and the so-called Kondo insulator compound YbB$_{12}$ and Yb-based Yb$_{x}R_{1-x}$B$_{12}$ solid solutions, on the other. The development of the cooperative dynamic Jahn-Teller instability of the covalent boron network produces trigonal and tetragonal distortions of the rigid cage and results in the symmetry lowering of the fcc lattice in the dodecaborides. The ferrodistortive dynamics in the boron sub-lattice generates both the collective modes and quasilocal vibrations (rattling modes) of the heavy RE ions, causing a modulation in the charge-carrier density and the emergence of dynamic charge stripes. We consider their manifestations both in the properties of the nonmagnetic reference compound LuB$_{12}$ and in the phase diagrams of the $R\mathrm{B}_{12}$ antiferromagnets that exhibit multiple magnetic phases with anisotropic field-angular phase diagrams in the form of the Maltese cross. We also discuss the metal-insulator transitions in YbB$_{12}$ and Yb-based dodecaborides in terms of the instability of the Yb 4$f$-electron configuration, which appears in addition to the Jahn-Teller instability of the boron cage, providing one more mechanism of the charge and spin fluctuations. The experimental results challenge the established Kondo-insulator scenario in YbB$_{12}$, providing arguments in favor of the appearance of Yb-Yb vibrationally coupled pairs which should be considered as the main factor responsible for the charge- and spin-gap formation.
The properties of the novel heavy fermion superconductor Ce$_3$PtIn$_{11}$ are investigated by thermodynamic and transport measurements at ambient and under hydrostatic pressure. At ambient pressure the compound exhibits two successive magnetic transitions at $T_1$ $\approx$ 2.2 K and $T_{\rm N}$ $\approx$ 2 K into antiferromagnetically ordered states and enters into a heavy fermion superconducting phase below $T_{\rm c}$ $\approx$ 0.32 K. The coexistence of long-range magnetic order and superconductivity is discussed in the context of the existence of the two crystallographically inequivalent…
We show that the interplay of a high density two-dimensional electron gas and localized electrons in a neighboring Mott insulator leads to kinetic magnetism unique to the Mott/band insulator interface. Our study is based upon a bilayer Hubbard model at $U=\infty$ with a potential difference between the two layers. We combine analytic results with DMRG simulations to show that magnetism, and especially ferromagnetism, is greatly enhanced relative by the proximity of the two subsystems. The results are potentially relevant to recent experiments suggesting magnetism in $R$TiO$_3$/SrTiO$_3$ hetero…
The continuous quantum phase transition and the nature of quantum critical point (QCP) in a modified Kondo lattice model with Ising anisotropic exchange interactions is studied within the density-matrix renormalization group algorithm. We investigate the effect of quantum fluctuations on critical Kondo destruction QCP, by probing static and dynamic properties of the magnetic order and the Kondo effect. In particular, we identify that local Kondo physics itself becomes critical at the magnetic phase transition point, providing unbiased evidences for local quantum criticality between two insulat…
Electrons undergoing a Mott transition may shed their charge but persist as neutral excitations of a quantum spin liquid (QSL). We introduce concrete two-dimensional models exhibiting this exotic behavior as they transition from superconducting or topological phases into fully charge-localized insulators. We study these Mott transitions and the confinement of neutral fermions at a second transition into a symmetry-broken phase. In the process, we also derive coupled-wire parent Hamiltonians for a non-Abelian QSL and a $\mathbb{Z}_4$ QSL.
Two phase transitions in the tetragonal strongly correlated electron system CeNiAsO were probed by neutron scattering and zero field muon spin rotation. For $T <T_{N1}$ = 8.7(3) K, a second order phase transition yields an incommensurate spin density wave with wave vector $\textbf{k} = (0.44(4), 0, 0)$. For $T < T_{N2}$ = 7.6(3) K, we find co-planar commensurate order with a moment of $0.37(5)~μ_B$, reduced to $30 \%$ of the saturation moment of the $|\pm\frac{1}{2}\rangle$ Kramers doublet ground state, which we establish by inelastic neutron scattering. Muon spin rotation in $\rm CeNiAs_{1-x}…
We develop an Eliashberg theory for multi-scale quantum criticality, considering ferromagnetic quantum criticality in the surface of three dimensional topological insulators. Although an analysis based on the random phase approximation has been performed for multi-scale quantum criticality, an extension to an Eliashberg framework was claimed to be far from triviality in respect that the self-energy correction beyond the random phase approximation, which originates from scattering with $z = 3$ longitudinal fluctuations, changes the dynamical exponent $z = 2$ in the transverse mode, explicitly d…
For D-dimensional weakly interacting topological insulators in certain symmetry classes, the topological invariant can be calculated from a D- or (D+1)-dimensional integration over a certain curvature function that is expressed in terms of single-particle Green's functions. Based on the divergence of curvature function at the topological phase transition, we demonstrate how a renormalization group approach circumvents these integrations and reduces the necessary calculation to that for the Green's function alone, rendering a numerically efficient tool to identify topological phase transitions …
We study topological crystalline insulators doped with magnetic impurities, in which ferromagnetism at the surface lowers the electronic energy by spontaneous breaking of a crystalline symmetry. The number of energetically equivalent ground states is sensitive to the crystalline symmetry of the surface, as well as the precise density of electrons at the surface. We show that for a SnTe model in the topological state, magnetic states can have twofold symmetry, sixfold symmetry, or eightfold degenerate minima. We compute spin stiffnesses within the model to demonstrate the stability of ferromagn…
We study the spin-1 honeycomb lattice magnets with frustrated exchange interactions. The proposed microscopic spin model contains first and second neighbor Heisenberg interactions as well as the single-ion anisotropy. We establish a rich phase diagram that includes a featureless quantum paramagnet and various spin spiral states induced by the mechanism of order by quantum disorder. Although the quantum paramagnet is dubbed featureless, it is shown that, the magnetic excitations develop a contour degeneracy in the reciprocal space at the band minima. These contour degenerate excitations are res…
The LDA+DMFT (local density approximation combined with dynamical mean-field theory) computation scheme has been used to study spectral and magnetic properties of FeSi and Fe$_{1-x}$Co$_{x}$Si. Having compared different models we conclude that a correlated band insulator scenario in contrast to Kondo insulator model agrees with FeSi band structure as well as experimental data. Coulomb correlation effects lead to band narrowing of the states near the Fermi level with mass renormalization parameter $m^*\approx 2$ in agreement with the results of angle-resolved photoemission spectroscopy (ARPES).…
Topological Kondo insulators are a rare example of an interaction-enabled topological phase of matter in three-dimensional crystals - making them an intriguing but also hard case for theoretical studies. Here, we aim to advance their theoretical understanding by solving the paradigmatic two-band model for topological Kondo-insulators using a fully spin-rotation invariant slave-boson treatment. Within a mean-field approximation, we map out the magnetic phase diagram and characterize both antiferromagnetic and paramagnetic phases by their topological properties. Among others, we identify an anti…
Experiments demonstrating the controlled growth of oxide heterostructures have raised the prospect of realizing topologically nontrivial states of correlated electrons in low dimensions. Here, we study heterostructures consisting of {111}-bilayers of double perovskites separated by inert band insulators. In bulk, these double perovskites have well-defined local moments interacting with itinerant electrons leading to high temperature ferromagnetism. Incorporating spin-orbit coupling in the two-dimensional honeycomb geometry of a {111}-bilayer, we find a rich phase diagram with tunable ferromagn…
We study the effects of electronic correlations on fragile topology using dynamical mean-field theory. Fragile topological insulators (FTIs) offer obstruction to the formation of exponentially localized Wannier functions, but they can be trivialized by adding certain trivial degrees of freedom. For the same reason, FTIs do not host symmetry-protected flow of edge states between bulk bands in cylindrical boundary conditions but are expected to have a spectral flow between the fragile bands and other bands under certain twisted boundary conditions. We here analyze commonly observed effects of st…
Electronic and magnetic structures of the newly synthesized cobalt oxyselenide La2Co2Se2O3 (structurally similar to the superconducting iron pnictides) are studied through density functional calculations. The obtained results show that this material is a Mott insulator, and that it has a very stable Co2+ high-spin ground state with a t2g-like orbital ordering, which is substantiated by the calculated crystal-field excitation energies. The square lattice of the Co2+ spins is found to have a strong antiferro (a weak ferro) magnetic coupling for the second nearest neighbors (2nn) via O (Se2) and …
We derive the effective heat current density operator for the strong-coupling regime of Mott insulators. Similarly to the case of the electric current density, the leading contribution to this effective operator is proportional to the local scalar spin chirality $\hatχ_{jkl}= \mathbf{S}_l\cdot\left(\mathbf{S}_j\times \mathbf{S}_k\right)$. This common form of the effective heat and electric current density operators leads to a novel cross response in Mott insulators. A heat current induces a distribution of orbital magnetic moments in systems containing loops of an odd number of hopping terms. …
Kondo insulators are predicted to undergo an insulator-to-metal transition under applied magnetic field, yet the extremely high fields required to date have prohibited a comprehensive investigation of the nature of this transition. Here we show that Ce3Bi4Pd3 provides an ideal platform for this investigation, owing to the unusually small magnetic field of B ~ 11 T required to overcome its Kondo insulating gap. Above Bc, we find a magnetic field-induced Fermi liquid state whose characteristic energy scale T_FL collapses near Bc in a manner indicative of a magnetic field-tuned quantum critical p…
In Mott insulators with the t^4_{2g} electronic configuration such as of Re^{3+}, Ru^{4+}, Os^{4+}, and Ir^{5+} ions, spin-orbit coupling dictates a Van Vleck-type nonmagnetic ground state with angular momentum J=0, and the magnetic response is governed by gapped singlet-triplet excitations. We derive the exchange interactions between these excitons and study their collective behavior on different lattices. In perovskites, a conventional Bose condensation of excitons into a magnetic state is found, while an unexpected one-dimensional behavior supporting spin-liquid states emerges in honeycomb …
The magnetism of Sr$_2$F$_2$Fe$_2$OS$_2$ was examined through neutron powder diffraction and thermodynamic and transport measurements. Quasi-two-dimensional magnetic order develops below $T_N$ = 106(2) K with an in-plane correlation length exceeding 310 Å and an out-of-plane correlation length of just 17(3) Å. The data are consistent with a two-k structure with $k_1$ = (1/2, 0, 1/2) and $k_2$ = (0, 1/2, 1/2) and an ordered moment of 3.3(1) $μ_B$ oriented along the in-plane components of k. This structure is composed of orthogonal AFM chains intersecting at super-exchange mediating O sites. Den…
We investigate the metal-insulator transition in the layered Ruddelsden Popper series of strontium iridates Srn+1IrnO3n+1. Tight-binding models of t2g orbitals for n = 1, 2, and infinity are constructed, and changes in band dispersion due to dimensionality and spin-orbit coupling are presented. Identifying the states near the Fermi level to be predominantly Jeff = 1/2, we use an effective Hubbard model to study the effect of correlations. Transitions from a metallic state to various magnetically ordered states at different critical interactions are obtained. A canted antiferromagnetic insulato…
We show, by means of low-energy muon spin rotation measurements, that few-unit-cells thick La(2)CuO(4) layers synthesized digitally by molecular beam epitaxy synthesis are antiferromagnetically ordered. Below a thickness of about 5 CuO(2) layers the long-range ordered state breaks down, and a magnetic state appears with enhanced quantum fluctuations and a reduced spin stiffness. This magnetic state can exist in close proximity (few Angstrom) to high-temperature superconducting layers, without transmitting supercurrents.
The deconfined quantum critical point, a prototype Landau-forbidden transition, could exist in principle in the phase transitions involving symmetry protected topological phase, however, examples of such kinds of transition in physical systems are rare beyond one-dimensional systems. Here, using density-matrix renormalization group calculation, we unveil a bosonic integer quantum Hall phase in two-dimensional correlated honeycomb lattice, by full identification of its internal structure from the topological $\mathbf{K}$ matrix. Moreover we demonstrate that imbalanced periodic chemical potentia…
Exploiting the entanglement concept within a matrix-product-state based infinite density-matrix renormalization group approach, we show that the spin-density-wave and bond-order-wave ground states of the one-dimensional half-filled extended Hubbard model give way to a symmetry-protected topological Haldane state in case an additional alternating ferromagnetic spin interaction is added. In the Haldane insulator the lowest entanglement level features a characteristic twofold degeneracy. Increasing the ratio between nearest-neighbor and local Coulomb interaction $V/U$, the enhancement of the enta…
In this paper, we study the fermionic excitations near the quantum criticality using gauge/gravity duality. This is motivated by exploring the Fermi surface evolution near the quantum criticality. We construct the gravity dual of "paramagnetic-nematic" phase transition in a continuum limit and study the Fermi surface evolution across this quantum phase transition. We find that there exists non-Fermi liquid with the Fermi surface in the "paramagnetic" phase and the Fermi surface disappears in the "nematic" phase.
The quantum critical point (QCP) in the archetypical heavy-fermion compound CeCu$_6$ doped by Au is described, accounting for the localized $4f$-electron of Ce, using realistic electronic structure calculations combined with dynamical mean-field theory (DMFT). Magnetism trends in Ce(Cu$_{1-ε}$Au$_ε$)$_6$ are compared with those in Co-doped CeCu$_{5}$, which resides on the non-ferromagnetic side of the composition space of one of the earliest rare-earth permanent magnet compounds, Ce(Co,Cu)$_5$. The construction of a realistic Doniach phase diagram shows that the system crosses over a magnetic …
The fine control of magnetism and electronic structure is crucial since the interplay between magnetism and band topology can lead to various novel magnetic topological states including axion insulators, magnetic Weyl semimetals and Chern insulators etc. Through crystal growth, transport, thermodynamic, neutron diffraction measurements, we show that with Sb-doping, the newly-discovered intrinsic antiferromagnetic topological insulator MnBi4Te7 evolves from antiferro-magnetic to ferromagnetic and then ferrimagnetic. We attribute this to the formation of Mn(Bi,Sb) antisites upon doping, which re…
This review article is devoted to the interplay between frustrated magnetism and quantum critical phenomena, covering both theoretical concepts and ideas as well as recent experimental developments in correlated-electron materials. The first part deals with local-moment magnetism in Mott insulators and the second part with frustration in metallic systems. In both cases, frustration can either induce exotic phases accompanied by exotic quantum critical points or lead to conventional ordering with unconventional crossover phenomena. In addition, the competition of multiple phases inherent to fru…
The nature of metal-insulator and magnetic transitions is still a subject under intense debate in condensed matter physics. Amongst the many possible mechanisms, the interplay between electronic correlations and spin-orbit couplings is an issue of a great deal of interest, in particular when dealing with quasi-2D compounds. In view of this, here we use a Hartree-Fock approach to investigate how the Rashba spin-orbit coupling, $V_\text{SO}$, affects the magnetic ordering provided by a Hubbard interaction, $U$, on a square lattice. At half-filling, we have found a sequence of transitions for inc…
The low and high-temperature phases of V$_4$O$_7$ have been studied by \textit{ab initio} calculations. At high temperature, all V atoms are electronically equivalent and the material is metallic. Charge and orbital ordering, associated with the distortions in the V pseudo-rutile chains, occur below the metal-insulator transition. Orbital ordering in the low-temperature phase, different in V$^{3+}$ and V$^{4+}$ chains, allows to explain the distortion pattern in the insulating phase of V$_4$O$_7$. The in-chain magnetic couplings in the low-temperature phase turn out to be antiferromagnetic, bu…
We study the orbitally frustrated singlet-triplet models that emerge in the context of spin-orbit coupled Mott insulators with $t_{2g}^4$ electronic configuration. In these compounds, low-energy magnetic degrees of freedom can be cast in terms of three-flavor "triplon" operators describing the transitions between spin-orbit entangled $J=0$ ionic ground state and excited $J=1$ levels. In contrast to a conventional, flavor-isotropic O(3) singlet-triplet models, spin-orbit entangled triplon interactions are flavor-and-bond selective and thus highly frustrated. In a honeycomb lattice, we find clos…
We demonstrate that the prototypical two-dimensional Chern insulator hosts exotic quantum multi-criticality in the presence of an appropriate periodic driving: a linear Dirac-like transition coexists with a nodal loop-like transition caused by emerging symmetries. The existence of multiple universality classes and scaling laws can be unambiguously captured by a single renormalization group approach based on the stroboscopic Floquet Hamiltonian, regardless of whether the topological transition is associated with the anomalous edge modes or not.
We report specific heat and neutron scattering experiments performed on the system Ce$_{1-x}$La$_{x}$Ru$_{2}$Si$_{2}$ on the magnetic side of its quantum critical phase diagram. The Kondo temperature does not vanish at the quantum phase transition and elastic scattering indicates a gradual localisation of the magnetism when $x$ increases in the ordered phase.
CrI3 is a two-dimensional ferromagnetic van der Waals material with a charge gap of 1.1-1.2 eV. In this study, the electronic structure and magnetism of CrI3 are investigated by using density functional theory and dynamical mean-field theory. Our calculations successfully reproduce a charge gap of 1.1 eV in the paramagnetic state when a Hund coupling JH = 0.7 eV is included with an on-site Hubbard U = 5 eV. In contrast, with a large U value of 8 eV and negligible Hund coupling JH, CrI3 is predicted to be a moderately correlated metal in the paramagnetic state. We conclude that CrI3 is a Mott-H…
We study the behaviour of electrons interacting with a classical magnetic background via a strong Hund coupling. The magnetic background results from a Hamiltonian which favours at low temperature the emergence of a phase with non-zero scalar chirality. The strong Hund's coupling combined with the total chirality of the classical spins induces in the electrons an effective flux which results in the realisation of a band structure with non zero Chern number. First, we consider as a magnetic background a classical spin system with spontaneous net chirality. We study the Density of States (DoS) a…
Dynamically driven interacting quantum many-body systems have the potential to exhibit properties that defy the laws of equilibrium statistical mechanics. A widely studied model is the impulsively driven antiferromagnetic Mott insulator, which is predicted to realize exotic transient phenomena including dynamical phase transitions into thermally forbidden states and highly non-thermal magnon distributions. However such far-from-equilibrium regimes, where conventional time-dependent Ginzburg-Landau descriptions fail, are experimentally challenging to prepare and to probe especially in solid sta…
We use synchrotron x-ray diffraction and electrical transport under pressure to probe both the magnetism and the structure of single crystal NiS2 across its Mott-Hubbard transition. In the insulator, the low-temperature antiferromagnetic order results from superexchange among correlated electrons and couples to a (1/2, 1/2, 1/2) superlattice distortion. Applying pressure suppresses the insulating state, but enhances the magnetism as the superexchange increases with decreasing lattice constant. By comparing our results under pressure to previous studies of doped crystals we show that this depen…
Magnetic exchange couplings can be tuned by coupling to periodic light, where the frequency and amplitude are typically varied: a process known as Floquet engineering. The polarization of the light is also important, and in this paper, we show how different polarizations, including several types of unpolarized light, can tune the exchange couplings in distinct ways. Using unpolarized light, for example, it is possible to tune the material without breaking either time-reversal or any lattice symmetries. To illustrate these effects generically, we consider single-band Hubbard models at half-fill…
Quantum criticality in Yb(Rh0.97Co0.03)2Si2 is investigated by means of resistivity and magnetoresistance. The partial substitution of Co leads to a stabilization of the magnetism as expected according to the application of chemical pressure for Yb systems. However, the signature of the Kondo-breakdown remains at the same position in the temperature-magnetic field phase diagram compared to stoichiometric YbRh2Si2. As a consequence, the Kondo-breakdown is situated within the antiferromagnetic phase. These results fit well within the global phase diagram under chemical pressure [1].
Strain tuning is increasingly being recognized as a clean tuning parameter to induce novel behavior in quantum matter. Motivated by the possibility of straining graphene up to $20$ percent, we investigate novel quantum criticality due to interplay between strain-induced anisotropic band structure and critical antiferromagnetic spin fluctuations (AFSF) in this setting. We detail how this interplay drives $(i)$ a quantum phase transition (QPT) between the Dirac-semimetal-incoherent pseudogapped metal-correlated insulator as a function of strain ($ε$), and $(ii)$ critical AFSF-driven divergent ne…
We study the phase diagram and quantum critical region of one of the fundamental models for electronic correlations: the periodic Anderson model. Employing the recently developed dynamical vertex approximation, we find a phase transition between a zero-temperature antiferromagnetic insulator and a Kondo insulator. In the quantum critical region, we determine a critical exponent $γ\!=\!2$ for the antiferromagnetic susceptibility. At higher temperatures, we have free spins with $γ\!=\!1$ instead, whereas at lower temperatures, there is an even stronger increase and suppression of the susceptibil…
We discuss the boundary critical behaviors of two dimensional quantum phase transitions with fractionalized degrees of freedom in the bulk, motivated by the fact that usually it is the $1d$ boundary that is exposed and can be conveniently probed in many experimental platforms. In particular, we mainly discuss boundary criticality of two examples: i. the quantum phase transition between a $2d$ $Z_2$ topological order and an ordered phase with spontaneous symmetry breaking; ii. the continuous quantum phase transition between metal and a particular type of Mott insulator (U(1) spin liquid). This …
Study of the combined effects of strong electronic correlations with spin-orbit coupling (SOC) represents a central issue in quantum materials research. Predicting emergent properties represents a huge theoretical problem since the presence of SOC implies that the spin is not a good quantum number. Existing theories propose the emergence of a multitude of exotic quantum phases, distinguishable by either local point symmetry breaking or local spin expectation values, even in materials with simple cubic crystal structure such as Ba$_2$NaOsO$_6$. Experimental tests of such theories by local probe…
Ground state properties of the spin$-1/2$ Falicov-Kimball model on a triangular lattice in the presence of uniform external magnetic field are explored. Both the orbital and the Zeeman field-induced effects are taken into account and in each unit cell only rational flux fractions are considered. Numerical results, obtained with the help of Monte Carlo simulation algorithm, reveal that the ground state properties strongly depend on the onsite Coulomb correlation between itinerant and localized electrons, orbital magnetic field as well as the Zeeman splitting. Strikingly, for the on-site Coulomb…
Exploration of low temperature phase transitions associated with quantum critical point is one of the most mystifying fields of research which is under intensive focus in recent times. In this work, through comprehensive experimental evidences, we report the possibility of achieving quantum criticality in the neighborhood of a magnetic field-tuned tricritical point separating paramagnetic, antiferromagnetic and metamagnetic phases in a magnetic insulator, DyVO4. Magnetic susceptibility and heat capacity indicate to the presence of a long-range second order antiferromagnetic transition at TN ~ …
Bad-Metal (BM) behavior featuring linear temperature dependence of the resistivity extending to well above the Mott-Ioffe-Regel (MIR) limit is often viewed as one of the key unresolved signatures of strong correlation. Here we associate the BM behavior with the Mott quantum criticality by examining a fully frustrated Hubbard model where all long-range magnetic orders are suppressed, and the Mott problem can be rigorously solved through Dynamical Mean-Field Theory. We show that for the doped Mott insulator regime, the coexistence dome and the associated first-order Mott metal-insulator transiti…
