In this paper we study transport properties of electrons on the two-dimensional honeycomb lattice. We consider a half-filled system in the vicinity of a symmetry-breaking transition from a semimetallic phase towards an insulating phase with either charge density or spin density wave order. The effect of either order is to break the sublattice inversion symmetry which induces a finite gap for the electronic single-particle excitations. Phenomenologically, such a scenario is described in the framework of a Gross-Neveu theory. We analyze two related formulations of the model by means of (i) a controlled renormalization group calculation and (ii) the large-N method, both of which in combination with a Boltzmann transport equation. We determine the quantum-critical conductivity and also discuss crossover behavior from quantum critical behavior into the insulating and/or the semimetallic phases. We find that at asymptotically low temperatures the quantum-critical conductivity is given by a temperature independent universal number. Over a large temperature window the temperature independent quantum critical conductivity is masked by a logarithmically temperature dependent contribution due to the marginally irrelevant long-range Coulomb interaction. We discuss possible origins of this peculiarity in the two complementary formulations of the model. Furthermore, we consider possible relations of our findings to recent experiments, with a special emphasis on the quantum-critical-to-insulator crossover. We find that our results are in remarkably good qualitative and quantitative agreement with a recent analysis of the data sets under the hypothesis of an underlying gap in the single-particle spectrum.
A semimetal-insulator transition in the Hubbard model on the honeycomb lattice is studied by using the dynamical mean field theory. Electrons in the honeycomb lattice resemble the Dirac electron liquid and for weak interactions the system is semimetal. With increasing the local interaction a semimetal-insulator transition occurs. We find a nonanalytical structure of the phase transition which consists of a first-order transition line ending in a second-order transition point and high-temperature crossover line. A phase separation of semimetal and insulator occurs at low temperatures. Maxwell c…
The Mott transition in honeycomb compounds with significant spin-orbit coupling is explored. At finite temperatures we identify a novel semimetallic phase located between a topological insulator and a topological Mott insulator. This semimetal is characterized by having no charge gap, no quasiparticles and gapped spin excitations with non-trivial topological properties. While charge conduction is incoherent involving mean-free paths violating the Mott-Ioffe-Regel limit, spin excitations can be transported ballistically along the edges giving rise to a quantized spin conductance. Such bad topol…
Semimetals, in which conduction and valence bands touch but do not form Fermi surfaces, have attracted considerable interest for their anomalous properties starting with the discovery of Dirac matter in graphene and other two-dimensional honeycomb materials. Here we introduce a family of three-dimensional honeycomb systems whose electronic band structures exhibit a variety of topological semimetals with Dirac nodal lines. We show that these nodal lines appear in varying numbers and mutual geometries, depending on the underlying lattice structure. They are stabilized, in most cases, by a combin…
It is shown that the semimetallic state of the two-dimensional honeycomb lattice with a point-like Fermi surface is unstable towards a canted antiferromagnetic insulator upon application of an in-plane magnetic field. This instability is already present at the mean-field level; the magnetic field shifts the up- and the down-spin cones in opposite directions thereby generating a finite density of states at the Fermi surface and a perfect nesting between the up- and the down-spin Fermi sheets. This perfect nesting triggers a canted antiferromagnetic insulating state. Our conclusions, based on me…
The Hubbard model on the honeycomb lattice undergoes a quantum phase transition from a semimetallic to a Mott insulating phase and from a disordered to an anti-ferromagnetically phase. We show that these transitions occur simultaneously and we calculate the critical coupling $U_c=3.835(14)$ as well as the critical exponents $ν=1.181(43)$ and $β=0.898(37)$ which are expected to fall into the $SU(2)$ Gross-Neveu universality class. For this we employ Hybrid Monte Carlo simulations, extrapolate the single particle gap and the spin structure factors to the thermodynamic and continuous time limits,…
The semimetal to antiferromagnet quantum phase transition of the Hubbard model on the honeycomb lattice has come to the forefront in the context of the proposal that a semimetal to spin liquid transition can occur before the transition to the antiferromagnetic phase. To study the semimetal to antiferromagnet transition, we generalize the two-particle self-consistent (TPSC) approach to the honeycomb lattice (a structure that can be realized in graphene for example). We show that the critical interaction strength where the transition occurs is $U_c/t=3.79\pm 0.01$ quite close to the value $U_c/t…
A polymorph of RuI$_3$ synthesized under high pressure was found to have a two-layered honeycomb structure. The resistivity of RuI$_3$ exhibits a semimetallic behavior, in contrast to insulating properties in $α$-RuCl$_3$. In addition, Pauli paramagnetic behavior was observed in the temperature dependence of a magnetic susceptibility and a nuclear spin-lattice relaxation rate 1/$T_1$. The band structure calculations indicate that contribution of the I 5$p$ components to the low-energy $t_\mathrm{2g}$ bands effectively decreases Coulomb repulsion, leading to semimetallic properties. The physica…
Using large-scale quantum Monte Carlo simulations, we exactly solve a model of Fermions hopping on the honeycomb lattice with cluster charge interactions, which has been proposed as an effective model with possible application to twisted bilayer graphene near half-filling. We find an interaction driven semimetal to insulator transition to an insulating phase consisting of a valence bond solid with Kekulé pattern. Finite size scaling reveals that the phase transition of the semimetal to Kekulé valence bond solid phase is continuous and belongs to chiral XY universality class.
We study the interplay of strong electron correlations and intra-triangle spin exchange at two-thirds filling of the single-orbital Hubbard model on the decorated honeycomb lattice using rotationally invariant slave bosons. We find that the spin exchange tunes between a spin-$1$ Mott insulator, a metal, and a spin-$0$ Mott insulator when the exchange is antiferromagnetic. The Mott insulators occur from effective intra-triangle multi-orbital interactions and are adiabatically connected to the ground state of an isolated triangle. An antiferromagnetic spin exchange, as determined by the Goodenou…
Recently, a concept of orthogonal metal has been introduced to reinterpret the disordered state of slave-spin representation in the Hubbard model as an exotic gapped metallic state. We have extended this concept to study the slave-spin representation of Hubbard model on the honeycomb lattice.[Phys. Rev. B \textbf{86}, 165134 (2012)] It is found that a novel gapped metallic state coined orthogonal Dirac semimetal is identified. Such state corresponds to the disordered phase of slave-spin and has the same thermal-dynamical and transport properties as Dirac semimetal but its singe-particle excita…
We study the interplay between spin-orbit coupling (SOC) and Coulomb repulsion in a Hubbard model on a decorated honeycomb lattice which leads to a plethora of phases. While a quantum spin hall insulator is stable at weak Coulomb repulsion and moderate SOC, a semimetallic phase emerges at large SOC in a broad range of Coulomb repulsion. This semimetallic phase has topological properties not observed in conventional metals such as a finite, non-quantized spin Hall conductivity. At large Coulomb repulsion and negligible spin-orbit coupling, electronic correlations stabilize a resonance valence b…
We study hard-core bosons on the honeycomb lattice in the presence of anisotropic nearest-neighbor repulsive interactions. Using a quantum Monte Carlo (QMC) technique, we extract the phase diagram of the model in terms of the filling and the anisotropy. At half-filling we find a dimer insulator phase near maximum anisotropy that is characterized by a finite topological entanglement entropy $\ln(2)/2$, indicative of a fractional quantum Hall state for bosons. We identify the presence of edge states and derive a QMC-based method to extract and verify their chirality. Remarkably, this phase arise…
The $t_{2g}$ orbitals of an edge-shared transition-metal oxide with a honeycomb lattice structure form dispersionless electronic bands when only hopping mediated by the edge-sharing oxygens is accessible. This is due to the formation of isolated quasimolecular orbitals (QMOs) in each hexagon, introduced recently by Mazin et al. [Phys. Rev. Lett. 109, 197201 (2012)], which stabilizes a band insulating phase for $t_{2g}^5$ systems. However, with help of the exact diagonalization method to treat the electron kinetics and correlations on an equal footing, we find that the QMOs are fragile against …
Phase transition in a honeycomb lattice is studied by the means of the two dimensional Hubbard model and the exact diagonalization dynamical mean field theory at zero temperature. At low energies, the dispersion relation is shown to be a linear function of the momentum. In the limit of weak interactions, the system is in the semi-metal phase. By increasing the on site interaction a semi-metal to insulator transition takes place in the paramagnetic phase. Calculation of double occupancy shows such a phase transition is of the second order. The respective phase transition point and critical on-s…
Realization and design of topological insulators emerging from electron correlations, called topological Mott insulators (TMIs), is pursued by using mean-field approximations as well as multi-variable variational Monte Carlo (MVMC) methods for Dirac electrons on honeycomb lattices. The topological insulator phases predicted in the previous studies by the mean-field approximation for an extended Hubbard model on the honeycomb lattice turn out to disappear, when we consider the possibility of a long-period charge-density-wave (CDW) order taking over the TMI phase. Nevertheless, we further show t…
Inspired by recent discovery of correlated insulating states in twisted bilayer graphene (TBG), we study a two-orbital Hubbard model on the honeycomb lattice with two electrons per unit cell. Based on the real-space density matrix renormalization group (DMRG) simulation, we identify a metal-insulator transition around $U_c/t=2.5\sim3$. In the vicinity of $U_c$, we find strong spin/orbital density wave fluctuations at commensurate wavevectors, accompanied by weaker incommensurate charge density wave (CDW) fluctuations. The spin/orbital density wave fluctuations are enhanced with increasing syst…
Based on the Cluster Perturbation solution of the Hubbard hamiltonian for a 2-D honeycomb lattice we present quasiparticle band structures of nanoribbons at half filling as a function of the on-site electron-electron repulsion. We show that at moderate values of e-e interaction ribbons with armachair shaped edges exhibit an unexpected semimetallic behavior, recovering the original insulating character only at larger values of $U$.
Describing correlated electron systems near phase transitions has been a major challenge in computational condensed-matter physics. In this paper, we apply highly accurate fixed node quantum Monte Carlo techniques, which directly work with many body wave functions and simulate electron correlations, to investigate the metal to insulator transition of a correlated hydrogen lattice. By calculating spin and charge properties, and analyzing the low energy Hilbert space, we identify the transition point and identify order parameters that can be used to detect the transition. Our results provide a b…
The Kitaev model, characterized by bond-dependent Ising spin interactions among spin-orbit entangled dipole moments in Mott insulators, offered a new approach to quantum spin liquids. Motivated by another type of bond-dependent interaction among quadrupole moments in $5d^2$ Mott insulators, we provide a microscopic route to uncover the Kitaev multipolar liquid, featuring fractionalized excitations out of non-Kramers doublets carrying multipole moments. The key ingredient is the magnetic field that allows for bond-anisotropic quadrupole-octupole interactions via mixing with the excited triplet …
A novel gapped metallic state coined orthogonal Dirac semimetal is proposed in the honeycomb lattice in terms of $Z_{2}$ slave-spin representation of Hubbard model. This state corresponds to the disordered phase of slave-spin and has the same thermaldynamical and transport properties as usual Dirac semimetal but its singe-particle excitation is gapped and has nontrivial topological order due to the $Z_{2}$ gauge structure. The quantum phase transition from this orthogonal Dirac semimetal to usual Dirac semimetal is described by a mean-field decoupling with complementary fluctuation analysis an…
We study a layered three-dimensional heterostructure in which two types of Kondo insulators are stacked alternatingly. One of them is the topological Kondo insulator SmB 6 , the other one an isostructural Kondo insulator AB 6 , where A is a rare-earth element, e.g., Eu, Yb, or Ce. We find that if the latter orders ferromagnetically, the heterostructure generically becomes a magnetic Weyl Kondo semimetal, while antiferromagnetic order can yield a magnetic Dirac Kondo semimetal. We detail both scenarios with general symmetry considerations as well as concrete tight-binding calcu-lations and show…
It has been recently shown that in the Heisenberg (anti)ferromagnet on the honeycomb lattice, the magnons (spin wave quasipacticles) realize a massless two-dimensional (2D) Dirac-like Hamiltonian. It was shown that the Dirac magnon Hamiltonian preserves time-reversal symmetry defined with the sublattice pseudo spins and the Dirac points are robust against magnon-magnon interactions. The Dirac points also occur at nonzero energy. In this paper, we propose a simple realization of nontrivial topology (magnon edge states) in this system. We show that the Dirac points are gapped when the inversion …
Nodal line semimetals are characterized by nontrivial bulk-band crossings, giving rise to almost flat drumhead-like surface states (DSS), which provide an attractive playground where interaction can induce symmetry-broken states and potential emergent phases. Here, we show that electronic interaction causes Stoner ferromagnetic instability in the DSS while the bulk remains non-magnetic, which together with spin-orbit coupling drive the surface states into a 2D Chern insulator. We show that each DSS carries a half-monopole charge, which for systems containing two pieces of DSS yield a net Chern…
Novel ground states might be realized in honeycomb lattices with strong spin-orbit coupling. Here we study the electronic structure of $α$-RuCl$_3$, in which the Ru ions are in a d5 configuration and form a honeycomb lattice, by angle-resolved photoemission, x-ray photoemission and electron energy loss spectroscopy supported by density functional theory and multiplet calculations. We find that $α$-RuCl$_3$ is a Mott insulator with significant spin-orbit coupling, whose low energy electronic structure is naturally mapped onto Jeff states. This makes $α$-RuCl$_3$ a promising candidate for the re…
We report structural studies of the spin-orbit Mott insulator family K$_x$Ir$_y$O$_2$, with triangular layers of edge-sharing IrO$_6$ octahedra bonded by potassium ions. The potassium content acts as a chemical tuning parameter to control the amount of charge in the Ir-O layers. Unlike the isostructural families with Ir replaced by Co or Rh ($y=1$), which are metallic over a range of potassium compositions $x$, we instead find insulating behaviour with charge neutrality achieved via iridium vacancies, which order in a honeycomb supercell above a critical composition $x_c$. By performing densit…
We study the spinless and spinful extended Hubbard models with repulsive interactions on the kagome and the decorated honeycomb ("star") lattice. Using Hartree-Fock mean-field theory, we show that interaction-driven insulating phases with non-trivial topological invariants (Chern number or $Z_2$ invariant) exist for an experimentally reasonable range of parameters. These phases occur at filling fractions which involve either Dirac points or quadratic band crossing points in the non-interacting limit. We present comprehensive mean-field phase diagrams for these lattices and discuss the competit…
The SU(4)-symmetric spin-orbital model on the honeycomb lattice was recently studied in connection to correlated insulators such as the $e_{g}$ Mott insulator Ba$_{3}$CuSb$_{2}$O$_{9}$ and the insulating phase of magic-angle twisted bilayer graphene at quarter filling. Here we provide a unified discussion of these systems by investigating an extended model that includes the effects of Hund's coupling and anisotropic, orbital-dependent exchange interactions. Using a combination of mean-field theory, linear flavor-wave theory, and variational Monte Carlo, we show that this model harbors a quantu…
We examine the role of spin-orbit coupling in the electronic structure of $α$-RuCl3, in which Ru ions in 4d5 configuration form a honeycomb lattice. The measured optical spectra exhibit a clear optical gap and excitations within the t2g orbitals. The spectra can be described very well with first-principles electronic structure calculations obtained by taking into account both spin orbit coupling and electron correlations. Furthermore, our X-ray absorption spectroscopy measurements at the Ru L-edges exhibit distinct spectral features associated with the presence of substantial spin- orbit coupl…
Ferromagnetism in the two-dimensional CrI$_3$ has generated a lot of excitement, and it was recently proposed that the spin-orbit coupling (SOC) in Iodine may generate bond-dependent spin interactions leading to magnetic anisotropy. Here we derive a microscopic spin model of S=3/2 on transition metals surrounded by heavy ligands in honeycomb Mott insulators using a strong-coupling perturbation theory. For ideal octahedra we find Heisenberg and Kitaev interactions, which favor the magnetic moment along the cubic axis via quantum fluctuations. When a slight trigonal distortion of the octahedra i…
In this paper, the honeycomb Hubbard model in optical lattices is investigated using O(3) non-linear sigma model. A possible quantum non-magnetic insulator in a narrow parameter region is found near the metal-insulator transition. We study the corresponding dynamics of magnetic properties, and find that the narrow region could be widened by hole doping.
The interaction-driven quantum anomalous Hall (QAH) insulator has been sought for a long time in a Dirac semimetal with linear band touching points at the Fermi level. By combining exact diagonalization, density matrix renormalization group, and analytical methods, we study a spinless fermion system on the checkerboard lattice with two fold rotational symmetry, which realizes two Dirac band touching points in the absence of interaction. At weak coupling, the Dirac semimetal is stable. At a finite density-density repulsive interaction, we analyze possible symmetry broken states, and find that a…
We study a two-dimensional fermionic square lattice, which supports the existence of two-dimensional Weyl semimetal, quantum anomalous Hall effect, and $2π$-flux topological semimetal in different parameter ranges. We show that the band degenerate points of the two-dimensional Weyl semimetal and $2π$-flux topological semimetal are protected by two distinct novel hidden symmetries, which both corresponds to antiunitary composite operations. When these hidden symmetries are broken, a gap opens between the conduction and valence bands, turning the system into a insulator. With appropriate paramet…
We show how to construct fully symmetric, gapped states without topological order on a honey- comb lattice for S = 1/2 spins using the language of projected entangled pair states(PEPS). An explicit example is given for the virtual bond dimension D = 4. Four distinct classes differing by lattice quantum numbers are found by applying the systematic classification scheme introduced by two of the authors [S. Jiang and Y. Ran, Phys. Rev. B 92, 104414 (2015)]. Lack of topological degeneracy or other conventional forms of symmetry breaking, and the existence of energy gap in the proposed wave functio…
We investigate the interacting Dirac fermions on honeycomb lattice by cluster dynamical mean-field theory (CDMFT) combined with continuous time quantum Monte Carlo simulation (CTQMC). A novel scenario for the semimetal-Mott insulator transition of the interacting Dirac fermions is found beyond the previous DMFT studies. We demonstrate that the non-local spatial correlations play a vital role in the Mott transition on the honeycomb lattice. We also elaborate the experimental protocol to observe this phase transition by the ultracold atoms on optical honeycomb lattice.
We study the single-orbital Hubbard model on the half-filled decorated honeycomb lattice. In the non-interacting theory at half-filling the Fermi energy lies within a flat band where strong correlations are enhanced. The lattice is highly frustrated. We find a correlation driven first-order metal-insulator transition to two different insulating ground states - a dimer valence bond solid Mott insulator when inter-triangle correlations dominate, and a broken $\mathcal{C}_3$-symmetry antiferromagnet that arises from frustration when intra-triangle correlations dominate. The metal-insulator transi…
The strong Coulomb interaction between massless Dirac fermions can drive a semimetal-insulator transition in single-layer graphene by dynamically generating an excitonic fermion gap. There is a critical interaction strength $λ_c$ that separates the semimetal phase from the insulator phase. We calculate the specific heat and susceptibility of the system and show that they exhibit distinct behaviors in the semimetal and insulator phases.
We study the Kane-Mele-Hubbard model with an additional inversion-symmetry-breaking term. Using the topological Hamiltonian approach, we calculate the $\mathbb{Z}_2$ invariant of the system as function of spin-orbit coupling, Hubbard interaction $U$, and inversion-symmetry-breaking on-site potential. The phase diagram calculated in that way shows that, on the one hand, a large term of the latter kind destroys the topological non-trivial state. On the other hand, however, this inversion-symmetry-breaking field can enhance the topological state, since for moderate values the transition from the …
We investigate the competition between the spin-orbit interaction of itinerant electrons and their Kondo coupling with local moments densely distributed on the honeycomb lattice. We find that the model at half-filling displays a quantum phase transition between topological and Kondo insulators at a nonzero Kondo coupling. In the Kondo-screened case, tuning the electron concentration can lead to a new topological insulator phase. The results suggest that the heavy-fermion phase diagram contains a new regime with a competition among topological, Kondo-coherent and magnetic states, and that the r…
We examine the effects of quantum fluctuations on a classical spin liquid state in the fully-frustrated honeycomb lattice Bose Hubbard model using quantum Monte Carlo simulations. Frustration is induced explicitly in the model by modulating the sign of the interaction spatially around each lattice hexagon. A superfluid to Mott insulating quantum phase transition can be induced by varying the relative strength of the classical interaction and quantum hopping. In the cases where the interaction has a regular spatial modulation, hopping promotes a phase transition to a symmetry-broken valence-bon…
Using density functional theory calculations with a Hubbard $U$, we explore topologically nontrivial phases in $X_2$O$_3$ honeycomb layers with $X=$ $4d$ and $5d$ cation inserted in the band insulator $α$-Al$_2$O$_3$ along the [0001]-direction. Several promising candidates for quantum anomalous Hall insulators (QAHI) are identified. In particular, for $X$=Tc and Pt spin-orbit coupling (SOC) opens a gap of 54 and 59 meV, respectively, leading to Chern insulators (CI) with $C$=--2 and --1. The nature of different Chern numbers is related to the corresponding spin textures. The Chern insulating p…
The low-energy theory of graphene exhibits spontaneous chiral symmetry breaking due to pairing of quasiparticles and holes, corresponding to a semimetal-insulator transition at strong Coulomb coupling. We report a Lattice Monte Carlo study of the critical exponents of this transition as a function of the number of Dirac flavors $N_f^{}$, finding $δ= 1.25 \pm 0.05$ for $N_f^{} = 0$, $δ= 2.26 \pm 0.06$ for $N_f^{} = 2$ and $δ= 2.62 \pm 0.11$ for $N_f^{} = 4$, with $γ\simeq 1$ throughout. We compare our results with recent analytical work for graphene and closely related systems, and discuss scen…
We take advantage of recent improvements in the grand canonical Hybrid Monte Carlo algorithm, to perform a precision study of the single-particle gap in the hexagonal Hubbard model, with on-site electron-electron interactions. After carefully controlled analyses of the Trotter error, the thermodynamic limit, and finite-size scaling with inverse temperature, we find a critical coupling of $U_c/κ=3.834(14)$ and the critical exponent $zν=1.185(43)$. Under the assumption that this corresponds to the expected anti-ferromagnetic Mott transition, we are also able to provide a preliminary estimate $β=…
A Dirac fermion emerges as a result of interplay between symmetry and topology in condensed matter. Current research moves towards investigating the Dirac fermions in the presence of manybody effects in correlated system. Here, we demonstrate the emergence of correlation-induced symmetry-protected Dirac semimetal state in the lightly-doped spin-orbit-coupled Mott insulator Sr$_2$IrO$_4$. We find that the nonsymmorphic crystalline symmetry stabilizes a Dirac line-node semimetal and that the correlation-induced symmetry-breaking electronic order further leads to a phase transition from the Dirac…
The fluctuations-driven continuous quantum criticality has sparked tremendous interest in condensed matter physics. It has been verified that the gapless fermions fluctuations can change the nature of phase transition at criticality. In this paper, we study the fermionic quantum criticality with enlarged Ising$\times$Ising fluctuations in honeycomb lattice materials. The Gross-Neveu-Yukawa theory for the multicriticality between the semimetallic phase and two ordered phases that break Ising symmetry is investigated by employing perturbative renormalization group approach. We first determine th…
The topological properties of hardcore bosons on ribbons of honeycomb lattice are studied using quantum Monte Carlo simulations. We map out a rich phase diagram with the superfluid and insulator phases at various fillings. Particularly, it is revealed that the insulator state at half filling is a topological bosonic state, which is characterized by a nontrivial Berry phase and a pair of edge states. We provide intuitive picture to understand this topological bosonic insulator state by showing that it can be adiabatically mapped to a topological fermionic model. It is also shown that the topolo…
We investigate the quantum many-body instabilities of the extended Hubbard model for spinless fermions on the honeycomb lattice with repulsive nearest-neighbor and 2nd nearest-neighbor density-density interactions. Recent exact diagonalization and infinite density matrix renormalization group results suggest that a putative topological Mott insulator phase driven by the 2nd nearest-neighbor repulsion is suppressed, while other numerically exact approaches support the topological Mott insulator scenario. In the present work, we employ the functional renormalization group (fRG) for correlated fe…
The excitonic insulator Ta$_2$NiSe$_5$ experiences a first-order structural transition under pressure from rippled to flat layer-structure at Ps = 3 GPa, which drives the system from an almost zero-gap semiconductor to a semimetal. The pressure-induced semimetal, with lowering temperature, experiences a transition to another semimetal with a partial-gap of 0.1-0.2 eV, accompanied with a monoclinic distortion analogous to that occurs at the excitonic transition below Ps. We argue that the partial-gap originates primarily from a symmetry-allowed hybridization of Ta-conduction and Ni-valence band…
Recent theoretical studies of topologically nontrivial electronic states in Kondo insulators have pointed to the importance of spin-orbit coupling (SOC) for stabilizing these states. However, systematic experimental studies that tune the SOC parameter $λ_{\rm{SOC}}$ in Kondo insulators remain elusive. The main reason is that variations of (chemical) pressure or doping strongly influence the Kondo coupling $J_{\text{K}}$ and the chemical potential $μ$ -- both essential parameters determining the ground state of the material -- and thus possible $λ_{\rm{SOC}}$ tuning effects have remained unnoti…
The Kitaev spin liquid, a ground state of the bond-dependent Kitaev model in a honeycomb lattice has been a centre of attraction, since a microscopic theory to realize such an interaction in solid-state materials was discovered. A challenge in real materials though is the presence of the Heisenberg and another bond-dependent Gamma interactions detrimental to the Kitaev spin liquid, and there have been many debates on their relative strengths. Here we offer a strategy to extract the Kitaev interaction out of a full microscopic model by utilizing the symmetries of the Hamiltonian. Two tilted mag…
The emergence of the Haldane Chern insulator state due to strong short range repulsive interactions in the half-filled fermionic spinless honeycomb lattice model has been proposed and challenged with different methods and yet it still remains controversial. In this work we revisit the problem using the infinite density matrix renormalization group method and report numerical evidence supporting i) the absence of the Chern insulator state, ii) two previously unnoticed charge ordered phases and iii) the existence and stability of all the non-topological competing orders that were found previousl…
We study the combined effects of lattice deformation, e-e interaction and spin-orbit coupling in a two-dimensional (2D) honeycomb lattice. We adopt different kinds of hopping modulation--generalized dimerization and a Kekule distortion--and calculate topological invariants for the non-interacting system and for the interacting system. We identify the parameter range (Hubbard U, hopping modulation, spin-orbit coupling) where the 2D system behaves as a trivial insulator or Quantum Spin Hall Insulator.
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 discuss the possibility of realizing Weyl semimetal phase in the magnetically doped topological band insulators. When the magnetic moments are ferromagnetically polarized, we show that there are three phases in the system upon the competition between topological mass and magnetic mass: topological band insulator phase, Weyl semimetal phase, and trivial phase. We explicitly derive the low energy theory of Weyl points from the general continuum Hamiltonian of topological insulators near the Dirac point, e.g. ${\bf k} \cdot {\bf p}$ theory near $Γ$ point for Bi_{2}Se_{3}. Furthermore, we intro…
According to Landau criterion, a phase transition should be first order when cubic terms of order parameters are allowed in its effective Ginzburg-Landau free energy. Recently, it was shown by renormalization group (RG) analysis that continuous transition can happen at putatively first-order $Z_3$ transitions in 2D Dirac semimetals and such non-Landau phase transitions were dubbed "fermion-induced quantum critical points" (FIQCP) [Li et al., Nature Communications 8, 314 (2017)]. The RG analysis, controlled by the 1/$N$ expansion with $N$ the number of flavors of four-component Dirac fermions, …
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…
We study a holographic model which exhibits a quantum phase transition from the strongly interacting Weyl semimetal phase to an insulating phase. In the holographic insulating phase there is a hard gap in the real part of frequency dependent diagonal conductivities. However, the anomalous Hall conductivity is nonzero at zero frequency, indicting that it is a Chern insulator. This holographic quantum phase transition is always of first order, signified by a discontinuous anomalous Hall conductivity at the phase transition, in contrast to the very continuous holographic Weyl semimetal/trivial se…
