We analyze the stability of excitonic ground states in the two-band Hubbard model with additional electron-phonon and Hund's rule couplings using a combination of mean-field and variational cluster approaches. We show that both the interband Coulomb interaction and the electron-phonon interaction will cooperatively stabilize a charge density wave (CDW) state which typifies an "excitonic" CDW if predominantly triggered by the effective interorbital electron-hole attraction or a "phononic" CDW if mostly caused by the coupling to the lattice degrees of freedom. By contrast, the Hund's rule coupling promotes an excitonic spin density wave. We determine the transition between excitonic charge and spin density waves and comment on a fixation of the phase of the excitonic order parameter that would prevent the formation of a superfluid condensate of excitons. The implications for exciton condensation in several material classes with strongly correlated electrons are discussed.
While excitonic instabilities in multiorbital systems recently have come under scrutiny in a variety of transition-metal compounds, understanding emergence of these instabilities from strong electronic interactions has remained a challenge. Here, we present a sign-problem-free determinant quantum Monte Carlo study of excitonic density orders in a half-filled two-orbital Hubbard-Kanamori model with broken orbital degeneracy, which accounts for the role of Hund's coupling in transition-metal compounds. For strong inverted (negative) Hund's exchange, we find numerical evidence for the emergence o…
We investigate the competition between the superconducting and the excitonic phases on Dirac electrons on a bipartite planar lattice. The conditions for the appearance of superconductivity or excitonic condensate are given by the minima of the free energy and our results are explained.
We study the disorder effect on the excitonic gap generation caused by strong Coulomb interaction in graphene. By solving the self-consistently coupled equations of dynamical fermion gap $m$ and disorder scattering rate $Γ$, we found a critical line on the plane of interaction strength $λ$ and disorder strength $g$. The phase diagram is divided into two regions: in the region with large $λ$ and small $g$, $m \neq 0$ and $Γ= 0$; in the other region, $m = 0$ and $Γ\neq 0$ for nonzero $g$. In particular, there is no coexistence of finite fermion gap and finite scattering rate. These results imply…
We investigate a problem about the competition between the hybridization and the Hund-rule coupling by applying the Wilson numerical renormalization-group method to the extended Kondo model where the impurity spin interacts via the Hund-rule coupling, with an extra spin which is isolated from the conduction electrons. It is shown that the Hund-rule coupling is an irrelevant perturbation against the strong coupling fixed point. However, the Hund-rule coupling decreases the characteristic energy $T_K$ drastically to the lower side and the irrelevant operator, which describes the low energy physi…
We consider a two-orbital Hubbard model with Hund coupling and crystal-field splitting and show that in the vicinity of the high-spin/low-spin transition, crystal-field quenches can induce an excitonic condensation at initial temperatures above the highest ordering temperature in equilibrium. This condensation is the effect of an increase in the spin entropy and an associated cooling of the effective electronic temperature. We identify a dynamical phase transition and show that such quenches can result in long-lived nonthermal excitonic condensates which have no analogue in the equilibrium pha…
Competition of crystal field splitting and Hund's rule coupling in magnetic metal-insulator transitions of half-filled two-orbital Hubbard model is investigated by multi-orbital slave-boson mean field theory. We show that with the increase of Coulomb correlation, the system firstly transits from a paramagnetic (PM) metal to a {\it Néel} antiferromagnetic (AFM) Mott insulator, or a nonmagnetic orbital insulator, depending on the competition of crystal field splitting and the Hund's rule coupling. The different AFM Mott insulator, PM metal and orbital insulating phase are none, partially and ful…
We study the ground-state properties of an extended periodic Anderson model to understand the role of Hund's coupling between localized and itinerant electrons using the density-matrix renormalization group algorithm. By calculating the von Neumann entropies we show that two phase transitions occur and two new phases appear as the hybridization is increased in the symmetric half-filled case due to the competition between Kondo-effect and Hund's coupling. In the intermediate phase, which is bounded by two critical points, we found a dimerized ground state, while in the other spatially homogeneo…
We examine the competition between the charge-density wave (CDW) instability and the excitonic condensate (EC) in spatially separated layers of electrons and holes. The CDW and the EC order parameters (OPs), described by two different mechanisms and hence two different transition temperatures $T^{CDW}_c$ and $T^{EC}_c$, are self-consistently coupled by a microscopic mean field theory. We discuss the results in our model specifically focusing on the transition-metal dichalcogenides which are considered as the most typical examples of strongly coupled CDW/EC systems with atomic layer separations…
A tight binding model is introduced to describe the strong interaction limit of excitonic ordering. At stoichiometry, the model reduces in the strong coupling limit to a pseudo-spin model with approximate U(4) symmetry. Excitonic order appears in the pseudo-spin model as in-plane pseudo-magnetism. The U(4) symmetry unifies all possible singlet and triplet order parameters describing such states. Super-exchange, Hunds-rule coupling, and other perturbations act as anisotropies splitting the U(4) manifold, ultimately stabilizing a paramagnetic triplet state. The tendency to ferromagnetism with do…
The competition between spin-orbit coupling $λ$ and electron-electron interaction $U$ leads to a plethora of novel states of matter, extensively studied in the context of $t_{2g}^4$ and $t_{2g}^5$ materials, such as ruthenates and iridates. Excitonic magnets -- the antiferromagnetic state of bounded electron-hole pairs -- is a prominent example of phenomena driven by those competing energy scales. Interestingly, recent theoretical studies predicted that excitonic magnets can be found in the ground-state of spin-orbit-coupled $t_{2g}^4$ Hubbard models. Here, we present a detailed computational …
Motivated by experimental developments introducing the concept of spin-orbit separation, we study the real-space time evolution of an excitonic wave-packet using a two-orbital Hubbard model. The exciton is created by exciting an electron from a lower energy half-filled orbital to a higher energy empty orbital. We carry out the real-time dynamics of the resulting excitonic wave-packet, using the time-dependent density matrix renormalization group method. We find clear evidence of charge-spin and spin-orbit separation in real-space, by tracking the time evolution of local observables. We show th…
The electronic properties of excitonic insulators have been examined precisely in recent years. Pictures of exciton condensation may be applied to the spin-state transition observed in perovskite cobalt oxides. We examine the crystal-field and magnetic-field dependences of spatial spin structures on the basis of the density matrix renormalization group method using an effective model for the one-dimensional two-orbital Hubbard model in strong-coupling limit. We find an excitonic insulating (EI) phase and a spin-state ordering (SSO) phase in the intermediate region between low-spin and high-spi…
Excitonic insulating system is studied from the viewpoints of the orbital physics in strongly correlated electron systems. An effective model Hamiltonian for low-energy electronic states is derived from the two-orbital Hubbard model with a finite energy difference corresponding to the crystalline field splitting. The effective model is represented by the spin operators and the pseudo-spin operators for the spin-state degrees of freedom. The ground state phase diagram is analyzed by the mean-field approximation. In addition to the low-spin state and high-spin state phases, two kinds of the exci…
Theoretical studies recently predicted the condensation of spin-orbit excitons at momentum $q$=$π$ in $t_{2g}^4$ spin-orbit coupled three-orbital Hubbard models at electronic density $n=4$. In parallel, experiments involving iridates with non-integer valence states for the Ir ions are starting to attract considerable attention. In this publication, using the density matrix renormalization group technique we present evidence for the existence of a novel excitonic condensate at $n=3.5$ in a one-dimensional Hubbard model with a degenerate $t_{2g}$ sector, when in the presence of spin-orbit coupli…
Magnetic competition in topological kagome magnets is studied by incorporating the spin-orbit coupling, the anisotropic Hund coupling and spin exchange into the kagome lattice. Using the Bogoliubov variational principle we find the stable phases at zero and finite temperatures. At zero temperature and in the strong Ising-Hund coupling regime, a magnetic tunability from the out-of-plane ferromagnetism (FM) to the in-plane antiferromagnetism (AFM) is achieved by a universal property of the critical in-plane Hund coupling. At two-thirds filling the phase transition from the out-of-plane FM to the…
We develop a theory of the excitonic phase recently proposed as the zero-field insulating state observed near charge neutrality in monolayer WTe$_2$. Using a Hartree-Fock approximation, we numerically identify two distinct gapped excitonic phases: a spin density wave state for weak non-zero interaction strength and spin spiral order at stronger interactions, separated by a narrow window of non-excitonic quantum spin Hall insulator. We introduce a simplified model capturing key features of the WTe$_2$ band structure, in which these phases appear as distinct valley ferromagnetic orders. We link …
We study the effect of Hund's splitting of repulsive interactions on electronic phase transitions in the multiorbital topological crystalline insulator Pb$_{1-x}$Sn$_{x}$Te, when the chemical potential is tuned to the vicinity of low-lying Type-II Van Hove singularities. Nontrivial Berry phases associated with the Bloch states impart momentum-dependence to electron interactions in the relevant band. We use a multipatch parquet renormalization group (RG) analysis for studying the competition of different electronic phases, and find that if the dominant fixed-point interactions correspond to ant…
We investigate few- and many-body states in half-filled maximally symmetric topological insulator flat bands realized by two degenerate Landau levels which experience opposite magnetic fields. This serves as a toy model of flat bands in moiré materials in which valleys have Chern numbers $C= \pm 1$. We argue that although the spontaneously polarized Ising Chern magnet is a natural ground state for repulsive Coulomb interactions, it can be in reasonable energetic competition with correlated states which can be viewed as Laughlin states of excitons when short distance corrections to the interact…
Effects of the spin-orbit coupling (SOC) and magnetic field on excitonic insulating (EI) states are investigated. We introduce the two-orbital Hubbard model with the crystalline field splitting, which is a minimal model for discussing the exciton condensation in strongly correlated electron systems, and analyze its effective Hamiltonian in the strong correlation limit by using the mean-field theory. In the absence of the SOC and magnetic field, the ground state changes from the nonmagnetic band-insulating state to the EI state by increasing the Hund coupling. In an applied magnetic field, the …
We propose a mechanism of the spin Seebeck effect attributed to excitonic condensation in a nonmagnetic insulator. We analyze a half-filled two-orbital Hubbard model with a crystalline field splitting in the strong coupling limit. In this model, the competition between the crystalline field and electron correlations brings about an excitonic insulating state, where the two orbitals are spontaneously hybridized. Using the generalized spin-wave theory and Boltzmann transport equation, we find that a spin current generated by a thermal gradient is observed in the excitonic insulating state withou…
We point out the generic competition between the Hund's coupling and the spin-orbit coupling in correlated materials, and this competition leads to an electronic dilemma between the Hund's metal and the relativistic insulators. Hund's metals refer to the fate of the would-be insulators where the Hund's coupling suppresses the correlation and drives the systems into correlated metals. Relativistic Mott insulators refer to the fate of the would-be metals where the relativistic spin-orbit coupling enhances the correlation and drives the systems into Mott insulators. These contradictory trends are…
Engineering non trivial topological phases in materials, specially skyrmion-like arrangements, has been of great interest in the last decade due to its potential technological applications. In this work, we study a model of electrons coupled to a magnetic texture in the kagome lattice interacting with magnetic moments via Rashba spin orbit coupling in the large Hund interaction limit. We obtain the effective spin Hamiltonian and study the emergent low temperature phases under an external magnetic field using large scale Monte Carlo simulations. We show that strong geometric frustration, charac…
Using a weak-coupling renormalization group formalism, we study competing ordered phases for repulsively interacting fermions on the bilayer honeycomb lattice away from half-filling, which is realized experimentally as doped bilayer graphene. As electrons are added to the system, excitonic order is suppressed, and unconventional superconductivity appears generically in its place. In general it is found that the maximum critical temperature for superconductivity appears directly adjacent to the dome of particle-hole order, illustrating the importance of fluctuations in these channels for the fo…
Competition between collective states like charge density wave and superconductivity is played out in some of the transition metal dichalcogenides unencumbered by the spin degrees of freedom. Although 2H-NbSe$_2$ has received much less attention than some of the other members of the family (like 1T-TiSe$_2$ and 2H-TaSe$_2$), it shows superconductivity at 7.2 K and incommensurate charge ordering at 33 K. Recent experiments, notably Angle Resolved Photoemission spectroscopy, have cast serious doubts on the mechanism of Fermi surface nesting via electron-phonon interaction. The normal state has b…
Hund's metals are multi-orbital systems with $3d$ or $4d$ electrons exhibiting both itinerant character and local moments, and they feature Kondo-like screenings of local orbital and spin moments, with suppressed coherence temperature driven by Hund's coupling $J_H$. They often exhibit magnetic order at low temperature, but how the interaction between the Kondo-like screening and long-range magnetic order is manifested in the quasiparticle spectrum remains an open question. Here we present spectroscopic signature of such interaction in a Hund's metal candidate MnSi exhibiting weak ferromagneti…
We investigate the quasiparticle dynamics in the two-orbital Hubbard model on the square lattice at quarter filling by means of the cellular dynamical mean field theory. We show that the Fermi-liquid state is stabilized up to the large Hubbard interactions in the symmetric case without the Hund's coupling, and find the heavy quasiparticles around the metal-insulator boundary. It is elucidated that the Hund's coupling enhances the antiferro-orbital correlations, which give rise to the pseudo gap behavior in the single-particle excitations. We also find the nonmonotonic temperature dependence in…
Using the Density Matrix Renormalization Group technique we study the effect of spin-orbit coupling on a three-orbital Hubbard model in the $(t_{2g})^{4}$ sector and in one dimension. Fixing the Hund coupling to a robust value compatible with some multiorbital materials, we present the phase diagram varying the Hubbard $U$ and spin-orbit coupling $λ$, at zero temperature. Our results are shown to be qualitatively similar to those recently reported using the Dynamical Mean Field Theory in higher dimensions, providing a robust basis to approximate many-body techniques. Among many results, we obs…
Hund's rule is one of the fundamentals of the correlation physics at the atomic level, determining the ground state multiplet of the electrons. It consists of three laws: (i) maximum $S$ (total spin), (ii) maximum $L$ (total orbital angular momentum) under the constraint of (i), and (iii) the total angular momentum $J$ is $|L-S|$ for electron number less than half, while $J=L+S$ for more than half due to the relativistic spin-orbit interaction (SOI). In real systems, the electrons hop between the atoms and gain the itinerancy, which is usually described by the band theory. The whole content of…
We use Ru $L_3$-edge (2838.5 eV) resonant inelastic x-ray scattering (RIXS) to quantify the electronic structure of Ca$_2$RuO$_4$, a layered $4d$-electron compound that exhibits a correlation-driven metal-insulator transition and unconventional antiferromagnetism. We observe a series of Ru intra-ionic transitions whose energies and intensities are well described by model calculations. In particular, we find a $\rm{J}=0\rightarrow 2$ spin-orbit excitation at 320 meV, as well as Hund's-rule driven $\rm{S}=1\rightarrow 0$ spin-state transitions at 750 and 1000 meV. The energy of these three featu…
The multi-orbital Hubbard model in one dimension is studied using the numerical diagonalization method. Due to the effect of the crystal-field splitting $Δ$, the fully polarized ferromagnetism which is observed in the strong coupling regime becomes unstable against the partially polarized ferromagnetism when the Hund's rule coupling $J$ is smaller than a certain critical value of order of $Δ$. In the vicinity of the partially polarized ferromagnetism, the orbital fluctuation develops due to the competition between the Hund's rule coupling and the crystal-field splitting. The superconducting ph…
We consider a model which includes the electron-phonon coupling to Ag or Jahn-Teller Hg phonons, the Coulomb interaction U and an exchange integral K. We study the metal-insulator transition for the integer fillings n=3 and 4. We find that the coupling to Ag phonons increases the critical value Uc where the transition takes place, while the coupling to Hg phonons decreases Uc. Without electron-phonon coupling the Hund's rule coupling also decreases Uc. There is, however, an interesting competition between the Hund's rule coupling and the Jahn-Teller effect. Thus the reduction of Uc due to the …
We present our theoretical results on the ground states in layered triangular-lattice compounds ANiO2 (A=Na, Li, Ag). To describe the interplay between charge, spin, orbital, and lattice degrees of freedom in these materials, we study a doubly-degenerate Hubbard model with electron-phonon couplings by the Hartree-Fock approximation combined with the adiabatic approximation. In a weakly-correlated region, we find a metallic state accompanied by \sqroot3x\sqroot3 charge ordering. On the other hand, we obtain an insulating phase with spin-ferro and orbital-ferro ordering in a wide range from inte…
On the basis of the multi-orbital dynamical mean field theory, a three-orbital Hubbard model with a relativistic spin-orbit coupling (SOC) is studied at five electrons per site. The numerical calculations are performed by employing the continuous-time quantum Monte Carlo (CTQMC) method based on the strong coupling expansion. We find that appropriately choosing bases, i.e., the maximally spin-orbit-entangled bases, drastically improve the sign problem in the CTQMC calculations, which enables us to treat exactly the full Hund's coupling and pair hopping terms. This improvement is also essential …
We present the first numerical study of the Falicov-Kimball model extended by an on-site hybridization away from the particle-hole symmetry point. Stable polaronic distortions of the charge-density wave (CDW) phase are observed when doping with a single hole. For moderate hole-doping, we find phase separation between a hole-rich homogeneous state and the usual CDW state. Excitonic order is enhanced around the hole-rich region, locally manifesting the global competition between this and the CDW phase. Associated with the hole-doping is a fractionalization of the electron density between the iti…
Different models for doping of two-orbital chains with mobile $S=1/2$ fermions and strong, ferromagnetic (FM) Hund's rule couplings stabilizing the S=1 spins are investigated by density matrix renormalization group (DMRG) methods. The competition between antiferromagnetic (AF) and FM order leads to a rich phase diagram with a narrow FM region for weak AF couplings and strongly enhanced triplet pairing correlations. Without a level difference between the orbitals, the spin gap persists upon doping, whereas gapless spin excitations are generated by interactions among itinerant polarons in the pr…
We study the interplay between the electron-electron (e-e) and the electron-phonon (e-ph) interactions in the two-orbital Hubbard-Holstein model at half filling using the dynamical mean field theory. We find that the e-ph interaction, even at weak couplings, strongly modifies the phase diagram of this model and introduces an orbital-selective Peierls insulating phase (OSPI) that is analogous to the widely studied orbital-selective Mott phase (OSMP). At small e-e and e-ph coupling, we find a competition between the OSMP and the OSPI, while at large couplings, a competition occurs between Mott a…
We explore the transition to a charge-disproportionated insulating phase in a five-orbital cubic tight-binding model applicable to transition-metal perovskites with a formal $d^4$ occupation of the transition-metal cation, such as ferrates or manganites. We use dynamical mean-field theory to obtain the phase diagram as a function of the average local Coulomb repulsion $U$ and the Hund's coupling $J$. The main structure of the phase diagram follows from the zero band-width (atomic) limit and represents the competition between high-spin and low-spin homogeneous and an inhomogeneous charge-dispro…
The lattice constant, bulk modulus and shear constant of TbN are calculated by means of density functional theory (DFT) in the local density approximation (LDA) and generalized gradient approximation (GGA), with 4f-states treated as valence electrons or core electrons. In addition, local Coulomb repulsions U are treated both statically as in the LDA+U approach and dynamically as in the dynamical mean-field theory (DMFT) in the Hubbard-I approximation. It is shown that all methods, except DFT-LDA with 4f electrons treated as either valence states, produce lattice constants and bulk moduli in go…
Complex oxides with $4d$ and $5d$ transition-metal ions recently emerged as a new paradigm in correlated electron physics, due to the interplay between spin-orbit coupling and electron interactions. For $4d$ and $5d$ ions, the spin-orbit coupling, $ζ$, can be as large as 0.2-0.4 eV, which is comparable with and often exceeds other relevant parameters such as Hund's coupling $J_{\rm H}$, noncubic crystal field splitting $Δ$, and the electron hopping amplitude $t$. This gives rise to a variety of spin-orbit-entangled degrees of freedom and, crucially, non-trivial interactions between them that d…
We study the three-orbital Kondo effect in quantum dot (QD) systems by applying the non-crossing approximation to the three-orbital Anderson impurity model. By investigating the tunneling conductance through a QD, we show that the competition between the Hund-coupling and the orbital level-splitting gives rise to characteristic behavior in transport properties. It is found that the Hund-coupling becomes more important in the three-orbital case than in the two-orbital case. We also show that the enhancement of Kondo temperature due to the singlet-triplet mechanism suggested for the two-orbital …
In this paper, we report the applicability of the density matrix renormalization group(DMRG) approach to the cylindrical single wall carbon nanotube (SWCN) for purpose of its correlation effect. By applying the DMRG approach to the $t$+$U$+$V$ model, with $t$ and $V$ being the hopping and Coulomb energies between the nearest neighboring sites, respectively, and $U$ the onsite Coulomb energy, we calculate the phase diagram for the SWCN with chiral numbers ($n_{1}=3, n_{2}=2$), which reflects the competition between the correlation energy $U$ and $V$. Within reasonable parameter ranges, we inves…
We show that the interplay of strong Hubbard interaction $U$ and spin-orbit coupling $λ$ in systems with $d^4$ electronic configuration leads to several unusual magnetic phases. Most notably, we find that competition between superexchange and spin-orbit coupling leads to a phase transition from a non-magnetic state predicted by atomic physics to a novel magnetic state in the large $U$ limit. We show that the local moment changes dramatically across this phase transition, challenging the conventional wisdom that local moments are robust against small perturbations in a Mott insulator. The Hund'…
We study the competing phases and the phase transition phenomena in an effective spin-orbital coupled model derived for pyroxene titanium oxides ATiSi2O6 (A=Na, Li). Using the mean-field-type analysis and the numerical quantum transfer matrix method, we show that the model exhibits two different ordered states, the spin-dimer and orbital-ferro state and the spin-ferro and orbital-antiferro state. The transition between two phases is driven by the relative strength of the Hund's-rule coupling to the onsite Coulomb repulsion and/or by the external magnetic field. The ground-state phase diagram i…
We investigate the phase diagram of an extended Kondo lattice model for doped manganese oxides in the presence of strong but finite Hund's coupling and on-site Coulomb interaction. By means of the Schwinger-boson mean-field approach, it is found that, besides magnetic ordering, there will be non-uniform charge distributions, such as charge ordering and phase separation, if the interaction between electrons prevails over the hybridization. Which of the charge ordering and phase separation appears is determined by a competition between effective repulsive and attractive interactions due to virtu…
Recently discovered advanced materials, such as heavy fermions, frequently exhibit a rich phase diagram suggesting the presence of different competing interactions. A unified description of the origin of these multiple interactions, albeit very important for the comprehension of such materials is, in general not available. It would be therefore very useful to have a simple model where the common source of different interactions could be possibly traced back. In this work we consider a system consisting in a set of localized spins on a square lattice with antiferromagnetic nearest neighbors int…
The recent detailed study of quasi-one-dimensional iron-based ladders, with the $3d$ iron electronic density $n = 6$, has unveiled surprises, such as orbital-selective phases. However, similar studies for $n=6$ iron chains are still rare. Here, a three-orbital electronic Hubbard model was constructed to study the magnetic and electronic properties of the quasi-one-dimensional $n=6$ iron chain Ce$_2$O$_2$FeSe$_2$, with focus on the effect of doping. Specifically, introducing the Hubbard $U$ and Hund $J_{H}$ couplings and studying the model via the density matrix renormalization group, we report…
Structural symmetry effects on the competition of density waves and superconductivity in bilayer nickelates
Ruhr-Universität Bochum（波鸿鲁尔大学）；Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所（北京凝聚态物理国家研究中心））；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
