The ground state of the bipartite $t$-$J$ model must satisfy a specific sign structure, based on which the single-hole and two-hole ground state $Ans\ddot{a}tze$ on honeycomb lattice are constructed and studied by a variational Monte Carlo (VMC) method. The VMC results are in good agreement with the exact diagonalization (ED) calculation. For the single-hole case, the degenerate ground states are characterized by quantum numbers of a spin-1/2 and an orbital angular momentum $L_z=\pm 2$. The latter is associated with the emergent chiral spin/hole currents mutually surrounding the hole/spin-1/2 as a composite object or ``twisted hole''. A vanishing quasiparticle spectral weight is shown in the large-sample limit. In the two-hole ground state, the holes form a spin-singlet pairing with $d$+$id$ symmetry in the Cooper channel, but are of $s$-wave symmetry as a tightly bound pair of the ``twisted holes''. Such a pairing mechanism of dichotomy can be attributed to eliminating the local spin currents which has nothing to do with the long-range antiferromagnetic correlation. Superconducting ground state at finite doping is briefly discussed in terms of the tightly bound hole pairs as the building blocks.
We show that as the result of the nesting property of the Fermi surface, the quarter-doped Hubbard model on honeycomb lattice is unstable with respect to the formation of a magnetic insulating state with nonzero spin chirality for infinitesimally small strength of electron correlation. The insulating state is found to be topological nontrivial and to have a quantized Hall conductance of $σ_{xy}=\frac{e^{2}}{h}$. We find the Fermi surface nesting is robust for arbitrary value of next-nearest-neighbor hopping integral. It is thus very possible that the quarter-doped graphene system will realize …
Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University（斯坦福材料能源科学研究所、SLAC国家加速器实验室和斯坦福大学）；Department of Physics and Astronomy, California State University, Northridge（加州州立大学北岭分校物理与天文学系）
We have performed large-scale density-matrix renormalization group studies of the lightly doped Hubbard model on the honeycomb lattice on long three and four-leg cylinders. We find that the ground state of the system upon lightly doping is consistent with that of a superconducting state with coexisting quasi-long-range superconducting and charge density wave orders. Both the superconducting and charge density wave correlations decay as a power law at long distances with corresponding exponents $K_{sc}<2$ and $K_c<2$. On the contrary, the spin-spin and single-particle correlations decay exponen…
We report the magnetic properties in the Co- and Zn-doped spin-1/2 honeycomb-lattice compound In$_3$Cu$_2$VO$_9$. The magnetic susceptibility and specific heat experiments show no long-range ordering down to 2 K in In$_3$Cu$_2$VO$_9$. In the low temperature range, approximately T$^{2}$-dependent magnetic specific heat and linearly T-dependent spin susceptibility were observed, suggesting a spin liquid candidate with a S = 1/2 honeycomb lattice. When Cu$^{2+}$ ions are partially substituted by Co$^{2+}$ ions, both impurity potential scattering and magnetic impurity scattering induced by magneti…
In extended Kitaev models on the honeycomb lattice, off-diagonal interactions (e.g. the $Γ, Γ^{'}$ terms) give rise to non-Kitaev quantum spin liquid (QSL) and several magnetically ordered phases. In the present work, we dope holes to the system and study the resultant $t$-$K$-$Γ$-$Γ^{'}$ model by mean field theory. The interplay between the charge and spin degrees of freedom results in a rich phase diagram. Similar to doped cuprates, superconductors, pseudogap phases, fermi liquid, strange metal and paramagnetic phase are generated. What is different is that, more than one superconducting pha…
A systematic low-energy effective field theory for hole-doped antiferromagnets on the honeycomb lattice is constructed. The formalism is then used to investigate spiral phases in the staggered magnetization as well as the formation of two-hole bound states.
We study the ground state properties of the doped Hubbard model with strong interactions on honeycomb lattice by the Density Matrix Renormalization Group (DMRG) method. At half-filling, due to the absence of minus sign problem, it is now well established by large-scale Quantum Monte Carlo calculations that a Dirac semi-metal to anti-ferromagnetic Mott insulator transition occurs with the increase of the interaction strength $U$ for the Hubbard model on honeycomb lattice. However, an understanding of the fate of the anti-ferromagnetic Mott insulator when holes are doped into the system is still…
In this work, a long-range resonating valence bond state is proposed as a variational wave function for the ground state of the $S=1/2$ antiferromagnetic Heisenberg model on the honeycomb lattice. Employing Variational Monte Carlo (VMC) method, we show that the ground state energy obtained from such RVB wave function, lies well below the energy of the Néel state and compares very well to the energies evaluated from spin-wave theory and series expansion method. We also obtain the spin-spin correlation function along zig-zag and armchair directions and find that the two correlations are differen…
Recently two interesting candidate quantum phases --- the chiral spin density wave state featuring anomalous quantum Hall effect and the d+id superconductor --- were proposed for the Hubbard model on the honeycomb lattice at 1/4 doping. Using a combination of exact diagonalization, density matrix renormalization group, the variational Monte Carlo method and quantum field theories, we study the quantum phase diagrams of both the Hubbard model and t-J model on the honeycomb lattice at 1/4-doping. The main advantage of our approach is the use of symmetry quantum numbers of ground state wavefuncti…
Using the low-energy effective field theory for hole-doped antiferromagnets on the honeycomb lattice, we study the localization of holes on Skyrmions, as a potential mechanism for the preformation of Cooper pairs. In contrast to the square lattice case, for the standard radial profile of the Skyrmion on the honeycomb lattice, only holes residing in one of the two hole pockets can get localized. This differs qualitatively from hole pairs bound by magnon exchange, which is most attractive between holes residing in different momentum space pockets. On the honeycomb lattice, magnon exchange unambi…
Motivated by possible applications to the antiferromagnetic precursor of the high-temperature superconductor Na$_x$CoO$_2\cdot$yH$_2$O, we use a systematic low-energy effective field theory for magnons and holes to study different phases of doped antiferromagnets on the honeycomb lattice. The effective action contains a leading single-derivative term, similar to the Shraiman-Siggia term in the square lattice case, which gives rise to spirals in the staggered magnetization. Depending on the values of the low-energy parameters, either a homogeneous phase with four or a spiral phase with two fill…
Tuning superconducting pairing symmetry via a staggered potential in the doped honeycomb Hubbard model
School of Physics and Astronomy, Beijing Normal University（北京师范大学物理学院）；Key Laboratory of Multiscale Spin Physics (Beijing Normal University), Ministry of Education（教育部多尺度自旋物理重点实验室（北京师范大学））；College of Physics, Hebei Normal University（河北师范大学物理学院）；Hebei Advanced Thin Films Laboratory（河北省先进薄膜实验室）
We develop a method of variational optimization of the infinite projected entangled pair states on the honeycomb lattice. The method is based on the automatic differentiation of the honeycomb-lattice corner transfer matrix renormalization group. We apply the approach to the antiferromagnetic Heisenberg spin-1/2 and ferromagnetic Kitaev models on the honeycomb lattice. The developed formalism gives quantitatively accurate results for the main physical observables and has a necessary potential for further extensions.
Using a controlled weak-coupling renormalization group approach, we establish the mechanism of unconventional superconductivity in the vicinity of spin or charge ordered excitonic states for the case of electrons on the Bernal stacked bilayer honeycomb lattice. With one electron per site this system exhibits nearly parabolically touching conduction and valence bands. Such a state is unstable towards a spontaneous symmetry breaking, and repulsive interactions favor excitonic order, such as a charge nematic and/or a layer antiferromagnet. We find that upon adding charge carriers to the system, t…
The emergence of superconductivity in doped Mott insulators has been debated for decades. In this paper, we report the theoretical discovery of a time-reversal symmetry breaking superconducting ground state in the doped Mott insulator (described by the well known t-J model) on honeycomb lattice, based on a recently developed variational method: the Grassmann tensor product state approach. As a benchmark, we use exact diagonalization and density-matrix renormalization methods to check our results on small clusters. We find systematic consistency for the ground-state energy as well as other phys…
We study the ground state of the doped Hubbard model on the honeycomb lattice in the small doping and strongly interacting region. The nature of the ground state by doping holes into the anti-ferromagnetic Mott insulating states on the honeycomb lattice remains a long-standing unsolved issue, even though tremendous efforts have been spent to investigate this challenging problem. An accurate determination of the ground state in this system is crucial to understand the interplay between the topology of Fermi surface and strong correlation effect. In this work, we employ two complementary, state-…
Motivated by recent discovery of correlated insulating and superconducting behavior in twisted bilayer graphene, we revisit graphene's honeycomb lattice doped close to the van Hove singularity, using the truncated unity functional renormalization group approach. We consider an extended Hubbard model on the honeycomb lattice including on-site and nearest-neighbor Coulomb repulsions, and nearest-neighbor ferromagnetic exchange and pair hopping interactions. By varying the strength of the nearest-neighbor exchange coupling and Coulomb repulsion as free parameters, we present rich ground-state pha…
Motivated by superconductivity (SC) in layered nitrides, we study an ionic-Hubbard model on a honeycomb lattice, which consists of two sublattices with an energy-level offset, by using an optimization variational Monte Carlo method. Parameter values for the Coulomb interaction and the energy-level offset, to realize a band insulator in non-doped state, are evaluated, and the SC state is investigated in a carrier-doped band insulator. It is found that, in a weakly doped band insulator, spin fluctuation remains and the spin-singlet d-wave SC state is realized. Present results support an unconven…
We get an anomalous Hall metallic state in the Honeycomb lattice with nearest neighbors only arising as a spontaneously broken symmetry state from a local nearest neighbor Coulomb interaction V . The key ingredient is to enlarge the unit cell to host six atoms that permits Kekulé distortions and supports self-consistent currents creating non trivial magnetic configurations with total zero flux. We find within a variational mean field approach a metallic phase with broken time reversal symmetry (T) very close in parameter space to a Pomeranchuk instability. Within the T broken region the predom…
We provide analytical and numerical evidence of a spin-triplet FFLO superconductivity in the itinerant Kitaev-Heisenberg model (anti-ferromagnetic Kitaev coupling and ferromagnetic Heisenberg coupling) on the honeycomb lattice around quarter filling. The strong spin-orbit coupling in our model leads to the emergence of 6 inversion symmetry centers for the Fermi surface at non zero momenta in the first Brillouin zone. We show how the Cooper pairs condense into these non-trivial momenta, causing the spatial modulation of the superconducting order parameter. Applying a Ginzburg-Landau expansion a…
Proposals for superconductivity emerging from correlated electrons in the doped Hubbard model on the honeycomb lattice range from chiral $d+id$ singlet to $p+ip$ triplet pairing, depending on the considered range of doping and interaction strength, as well as the approach used to analyze the pairing instabilities. Here, we consider these scenarios using large-scale dynamic cluster approximation (DCA) calculations to examine the evolution in the leading pairing symmetry from weak to intermediate coupling strength. These calculations focus on doping levels around the van Hove singularity (VHS) a…
By using the constrained-phase quantum Monte Carlo method, we performed a systematic study of the pairing correlations in the ground state of the doped Kane-Mele-Hubbard model on a honeycomb lattice. We find that pairing correlations with $d+id$ symmetry dominate close to half filling, but pairing correlations with $p+ip$ symmetry dominate as hole doping moves the system below three-quarters filling. We correlate these behaviors of the pairing correlations with the topology of the Fermi surfaces of the non-interacting problem. We also find that the effective pairing correlation is enhanced gre…
Motivated by the recent numerical simulations for doped $t$-$J$ model on the honeycomb lattice, we study superconductivity of singlet and triplet pairing on the honeycomb lattice Hubbard model. We show that a superconducting state with coexisting spin-singlet and spin-triplet pairings is induced by the antiferromagnetic order near half filling. The superconducting state we obtain has a topological phase transition that separates a topologically trivial state and a nontrivial state with Chern number two. Possible experimental realization of such a topological superconductivity is also discussed…
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…
We report staggered vorticity correlations of current in the d-wave variational wave function for the lightly-doped t-J model. Such correlations are explained from the SU(2) symmetry relating d-wave and staggered-flux mean-field phases. The correlation functions computed by the variational Monte Carlo method suggest that pairs are formed of holes circulating in opposite directions.
It is shown that the unique sign structure of the ground state of the Hubbard model on honeycomb lattice, which is shown to be insensitive to the trapped $Z_{2}$ gauge flux when the system is defined on a torus, may cause the absence of topological degeneracy on this bipartite system. Examples of variational Mott insulating state on the honeycomb lattice are given to illustrate the close relation between the sign structure of the ground state and the (absence of) topological degeneracy.
A quantum spin-liquid might be realized in $α$-RuCl$_{3}$, a honeycomb-lattice magnetic material with substantial spin-orbit coupling. Moreover, $α$-RuCl$_{3}$ is a Mott insulator, which implies the possibility that novel exotic phases occur upon doping. Here, we study the electronic structure of this material when intercalated with potassium by photoemission spectroscopy, electron energy loss spectroscopy, and density functional theory calculations. We obtain a stable stoichiometry at K$_{0.5}$RuCl$_3$. This gives rise to a peculiar charge disproportionation into formally Ru$^{2+}$ (4$d^6$) a…
Based on a symmetry analysis of the microscopic Hubbard and t-J models, a systematic low-energy effective field theory is constructed for hole-doped antiferromagnets on the honeycomb lattice. In the antiferromagnetic phase, doped holes are massive due to the spontaneous breakdown of the $SU(2)_s$ symmetry, just as nucleons in QCD pick up their mass from spontaneous chiral symmetry breaking. In the broken phase the effective action contains a single-derivative term, similar to the Shraiman-Siggia term in the square lattice case. Interestingly, an accidental continuous spatial rotation symmetry …
We present variational Monte Carlo (VMC) results for the Gutzwiller-projected coexisting state including both antiferromagnetic (AFM) order and superconducting (SC) order in the two-dimensional t-t'-t"-J model. By further considering off-site spin correlation between electrons, in contrast to earlier VMC results [Phys. Rev. Lett. 102, 027002 (2009)], we find the apparent competition between AFM order and SC order near the underdoped regime instead of coexistence. The local ferromagnetic correlation introduced by spin-spin Jastrow correlators seem to be responsible for the disappearance of the …
The possible emergence of a spin liquid phase in the half-filled Hubbard model on the honeycomb lattice; a simple model of graphene, is studied using the variational cluster approximation. We found that the critical interaction strength of a magnetic transition is slightly lower than that of the non-magnetic metal-to-insulator transition. Thus a semi-metallic state becomes a magnetic insulator as the interaction strength increases and a non-magnetic insulating state does not occur. Therefore a spin liquid state characterized by an insulating state without long range order, is not realized in t…
We study the ground-state phase diagram of the quantum $J_1-J_2$ model on the honeycomb lattice by means of an entangled-plaquette variational ansatz. Values of energy and relevant order parameters are computed in the range $0\le {J_2}/{J_1} \le 1$. The system displays classical order for ${J_2}/{J_1}\lesssim 0.2$ (Néel), and for $J_2/J_1 \gtrsim 0.4$ (collinear). In the intermediate region, the ground-state is disordered. Our results show that the reduction of the half-filled Hubbard model to the model studied here does not yield accurate predictions.
We examine the stability of classical states with a generic incommensurate spiral order against quantum fluctuations. Specifically, we focus on the frustrated spin-1/2 $XY$ and Heisenberg models on the honeycomb lattice with nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ antiferromagnetic couplings. Our variational approach is based on the Jastrow wave functions, which include quantum correlations on top of classical spin waves. We perform a systematic optimization of wave vectors and Jastrow pseudo-potentials within this class of variational states and find that quantum fluctuations f…
Polaron spectral functions are computed for highly doped graphene-on-substrate and other atomically thin graphitic systems using the diagrammatic Monte Carlo technique. The specific aim is to investigate the effects of interaction on spectral functions when the symmetry between sub-lattices of a honeycomb lattice has been broken by the substrate or ionicity, inducing a band gap. Introduction of electron-phonon coupling leads to several polaronic features, such as band-flattening and changes in particle lifetimes. At the K point, differences between energies on each sub-lattice increase with el…
We have performed extensive density matrix renormalization group (DMRG) studies of the Hubbard model on a honeycomb ladder. The band structure (with Hubbard U=0) exhibits an unusual quadratic band touching at half filling, which is associated with a quantum Lifshitz transition from a band insulator to a metal. %SAK as a function of a third-neighbor hopping parameter. For one electron per site, non-zero $U$ drives the system into an insulating state in which there is no pair-binding between added electrons; this implies that superconductivity driven directly by the repulsive electron-electron i…
A multi-reference configuration mixing scheme is used to describe the ground state, characterized by well defined spin and space group symmetry quantum numbers as well as doping fractions $N_{e}/N_{sites}$, of one dimensional Hubbard lattices with nearest-neighbor hopping and periodic boundary conditions. Within this scheme, each ground state is expanded in a given number of nonorthogonal and variationally determined symmetry-projected configurations. The results obtained for the ground state and correlation energies of half-filled and doped lattices with 30, 34 and 50 sites, compare well with…
Spontaneous charge ordering occurring in correlated systems may be considered as a possible route to generate effective lattice structures with unconventional couplings. For this purpose we investigate the phase diagram of doped extended Hubbard models on two lattices: (i) the honeycomb lattice with on-site $U$ and nearest-neighbor $V$ Coulomb interactions at $3/4$ filling ($n=3/2$) and (ii) the triangular lattice with on-site $U$, nearest-neighbor $V$, and next-nearest-neighbor $V'$ Coulomb interactions at $3/8$ filling ($n=3/4$). We consider various approaches including mean-field approximat…
We study the quantum many-body instabilities of the $t -J_{\mathrm{K}} - J_{\mathrm{H}}$ Kitaev-Heisenberg Hamiltonian on the honeycomb lattice as a minimal model for a doped spin-orbit Mott insulator. This spin-$1/2$ model is believed to describe the magnetic properties of the layered transition-metal oxide Na$_2$IrO$_3$. We determine the ground-state of the system with finite charge-carrier density from the functional renormalization group (fRG) for correlated fermionic systems. To this end, we derive fRG flow-equations adapted to the lack of full spin-rotational invariance in the fermionic …
Quantum phase transitions in the Hubbard model on the honeycomb lattice are investigated in the variational cluster approximation. The critical interaction for the paramagnetic to antiferromagnetic phase transition is found to be in remarkable agreement with a recent large-scale quantum Monte Carlo simulation. Calculated staggered magnetization increases continuously with $U$ and thus we find the phase transition is of a second order. We also find that the semimetal-insulator transition occurs at infinitesimally small interaction and thus a paramagnetic insulating state appears in a wide inter…
The physical nature of doped Mott-insulator has been intensively studied for more than three decades. It is well known that the single band Hubbard model or $t$-$J$ model on the bipartite lattice is the simplest model to describe a doped Mott insulator. Unfortunately, the key mechanism of superconductivity in these toy models is still under debate. In this paper, we propose a new mechanism for the $d+id$-wave superconductivity (SC) that occurs in the small-doping region of the honeycomb lattice $t$-$J$ model based on the Grassmann tensor product state numerical simulation and spin-charge separ…
Modification of interatomic distances due to high pressure leads to exotic phenomena, including metallicity, superconductivity and magnetism, observed in materials not showing such properties in normal conditions. In two-dimensional crystals, such as graphene, atomic bond lengths can be modified by more that 10 percent by applying in-plane strain, i.e., without generating high pressure in the bulk. In this work, we study the strain-induced Mott transition on a honeycomb lattice by using computationally inexpensive techniques, including Gutzwiller Wave Function (GWF) and different variants of G…
We study the phase diagram of the frustrated XY model on the honeycomb lattice by using accurate correlated wave functions and variational Monte Carlo simulations. Our results suggest that a spin-liquid state is energetically favorable in the region of intermediate frustration, intervening between two magnetically ordered phases. The latter ones are represented by classically ordered states supplemented with a long-range Jastrow factor, which includes relevant correlations and dramatically improves the description provided by the purely classical solution of the model. The construction of the …
We study the presence of ferromagnetism in the phase diagram of the two-dimensional honeycomb lattice close to half-filling (graphene) as a function of the strength of the Coulomb interaction and doping. We show that exchange interactions between Dirac fermions can stabilize a ferromagnetic phase at low doping when the coupling is sufficiently large. In clean systems, the zero temperature phase diagram shows both first order and second order transition lines and two distinct ferromagnetic phases: one phase with only one type of carriers (either electrons or holes) and another with two types of…
The magnetic structures and spin dynamics of Na$_{2}$Co$_{2}$TeO$_{6}$ and Na$_{2}$Ni$_{2}$TeO$_{6}$ are investigated by means of elastic and inelastic neutron scattering measurements and the results are discussed in the context of a generalized Kitaev-Heisenberg model on honeycomb lattice with strong spin-orbit coupling. The large number of parameters involved in the Hamiltonian model are evaluated by using an iterative optimization algorithm capable of extracting model solutions and simultaneously estimating their uncertainty. The analyses establish that both Co$^{2+}$ ($d^7$) and Ni$^{2+}$ …
In addition to the Kitaev ($K$) interaction, candidate Kitaev materials also possess Heisenberg ($J$) and off-diagonal symmetric ($Γ$) couplings. We investigate the quantum ($S = 1/2$) $K$-$J$-$Γ$ model on the honeycomb lattice by a variational Monte Carlo (VMC) method. In addition to the "generic" Kitaev spin liquid (KSL), we find that there is just one proximate KSL (PKSL) phase, while the rest of the phase diagram contains different magnetically ordered states. The PKSL is a gapless Z$_2$ state with 14 Majorana cones, which in contrast to the KSL has a gapless spin response. In a magnetic f…
The kinetic features of holes (electrons) in the Hubbard model are studied using a variational Monte Carlo method. In doped Mott insulators (U>U_co), holes are classified, in the sense of conduction, into two categories: (i) The holes appearing in doublon-holon pairs are localized, encourage singlet pair formation, and gain the energy to induce a superconducting transition. (ii) The doped holes become carriers, make the system itinerant (superconducting or metallic), but lose the energy in the transition. These two roles are distinguished in correlated superconductivity. This feature is common…
We investigate the properties of the nearest-neighbor singlet pairing and the emergence of d-wave superconductivity in the doped honeycomb lattice considering the limit of large interactions and the $t-J_1-J_2$ model. First, by applying a renormalized mean-field procedure as well as slave-boson theories which account for the proximity to the Mott insulating state, we confirm the emergence of d-wave superconductivity in agreement with earlier works. We show that a small but finite $J_2$ spin coupling between next-nearest neighbors stabilizes d-wave symmetry compared to the extended s-wave scena…
We study spontaneous symmetry breaking in a system of spinless fermions in the Honeycomb lattice paying special emphasis to the role of an enlarged unit cell on time reversal symmetry broken phases. We use a tight binding model with nearest neighbor hopping t and Hubbard interaction V1 and V2 and extract the phase diagram as a function of electron density and interaction within a mean field variational approach. The analysis completes the previous work done in Phys. Rev. Lett. 107, 106402 (2011) where phases with non--trivial topological properties were found with only a nearest neighbor inter…
We show the chiral d-wave RVB state on honeycomb lattice stands as a natural generalization of the staggered flux phase on square lattice. Although the state is generated from a time reversal symmetry broken mean field ansatz, it actually represents a fully symmetric spin liquid state with a positive definite wave function in the sense of Marshall sign rule for unfrustrated antiferromagnets. The evolution of the state with the parameter $Δ/χ$ follows exactly the same manner as that of the staggered flux phase on square lattice. The critical pairing strength corresponding to the $π$-flux phase …
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…
Using variational wave functions and Monte Carlo techniques, we study the antiferromagnetic Heisenberg model with first-neighbor $J_1$ and second-neighbor $J_2$ antiferromagnetic couplings on the honeycomb lattice. We perform a systematic comparison of magnetically ordered and nonmagnetic states (spin liquids and valence-bond solids) to obtain the ground-state phase diagram. Néel order is stabilized for small values of the frustrating second-neighbor coupling. Increasing the ratio $J_2/J_1$, we find strong evidence for a continuous transition to a nonmagnetic phase at $J_2/J_1 \approx 0.23$. C…
Motivated by the recently synthesized insulating nickelate Ni$_2$Mo$_3$O$_8$, which has been reported to have an unusual non-collinear magnetic order of Ni$^{2+}$ $S=1$ moments with a nontrivial angle between adjacent spins, we construct an effective spin-1 model on the honeycomb lattice, with the exchange parameters determined with the help of first principles electronic structure calculations. The resulting bilinear-biquadratic model, supplemented with the realistic crystal-field induced anisotropy, favors the collinear Néel state. We find that the crucial key to explaining the observed nonc…
We explore the possibility of inducing a topological insulator phase in a honeycomb lattice lacking spin-orbit interaction using a metallic (or Fermi gas) environment. The lattice and the metallic environment interact through a density-density interaction without particle tunneling, and integrating out the metallic environment produces a honeycomb sheet with in-plane oscillating long-ranged interactions. We find the ground state of the interacting system in a variational mean-field method and show that the Fermi wave vector, kF, of the metal determines which phase occurs in the honeycomb latti…
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…
Conflicting predictions have been made for the ground state of the SU(3) Heisenberg model on the honeycomb lattice: Tensor network simulations found a plaquette order [Zhao et al, Phys. Rev. B 85, 134416 (2012)], where singlets are formed on hexagons, while linear flavor-wave theory (LFWT) suggested a dimerized, color ordered state [Lee and Yang, Phys. Rev. B 85, 100402 (2012)]. In this work we show that the former state is the true ground state by a systematic study with infinite projected-entangled pair states (iPEPS), for which the accuracy can be systematically controlled by the so-called …
