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 density functional theory calculations we attribute the observed behaviour to a subtle interplay of crystal-field environment, local electronic correlations and strong spin-orbit interaction at the Ir$^{4+}$ sites, making this structural family a candidate to display Kitaev magnetism in the experimentally unexplored regime that interpolates between triangular and honeycomb structures.
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…
The Kitaev-Heisenberg model defined on both honeycomb and triangular lattices has been studied intensively in recent years as a possible model to describe spin-orbital physics in iridium oxides. In the model, there are many phases characteristic for each lattice. However, there is no study how the phases in the two lattices merge each other when geometry changes from honeycomb lattice to triangular lattice. We investigate the ground state of the Kitaev-Heisenberg model defined on the system connecting the honeycomb and triangular lattices, named a honeycomb-triangular lattice. We obtain a grou…
We propose that spin-fluctuation-mediated spin-triplet superconductivity may be realized in repulsive Hubbard models with disconnected Fermi surfaces. The idea is confirmed for Hubbard models on triangular (dilute band filling) and honeycomb (near half-filling) lattices using fluctuation exchange approximation, where triplet pairing order parameter with f-wave symmetry is obtained. Possible relevance to real superconductors is suggested.
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…
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…
We use finite temperature strong coupling expansions to calculate thermodynamic properties of the Honeycomb-lattice SU(4) Hubbard model. We present numerical results for various properties including chemical potential, compressibility, entropy and specific heat as a function of temperature and density at several $U/t$ values. We study the onset of charge incompressibility and Mott gaps as the temperature is lowered at integer densities. In the incompressible Mott regime, the expansions are recast into a high temperature expansion for a generalized spin model with SU(4) symmetry, which is then …
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 …
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…
The temperature-magnetic-field phase diagram of the mixed honeycomb triangular lattice system K$_{2}$Mn$_{3}$(VO$_{4}$)$_{2}$CO$_{3}$ is investigated by means of magnetization, heat capacity and neutron scattering measurements. The results indicate that triangular and honeycomb magnetic layers undergo sequential magnetic orderings and act as nearly independent magnetic sublattices. The honeycomb sublattice orders at about 85 K in a Neél-type antiferromagnetic structure, while the triangular sublattice displays two consecutive ordered states at much lower temperatures, 3 K and 2.2 K. The ground…
We use a projective symmetry group analysis to determine all symmetric spin liquids on the stuffed honeycomb lattice Heisenberg model. This lattice interpolates between honeycomb, triangular and dice lattices, always preserving hexagonal symmetry, and it already has one spin liquid candidate, TbInO$_3$, albeit with strong spin-orbit coupling not considered here. In addition to the stuffed honeycomb lattice itself, we gain valuable insight into potential spin liquids on the honeycomb and triangular lattices, as well as how they might be connected. For example, the sublattice pairing state propo…
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…
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,…
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…
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 investigate the competition between charge-density-wave (CDW) states and a Coulomb interaction-driven topological Mott insulator (TMI) in the honeycomb extended Hubbard model. For the spinful model with on-site ($U$) and next-nearest-neighbor ($V_2$) Coulomb interactions at half filling, we find two peculiar six-sublattice charge-density-wave insulating states by using variational Monte Carlo simulations as well as the Hartree-Fock approximation. We observe that conventional ordered states always win with respect to the TMI. The ground state is given in the large-$V_2$ region by a CDW chara…
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 …
We investigate the Hubbard model on the anisotropic triangular lattice by means of the cellular dynamical mean field theory. The phase diagram determined in the Hubbard interaction versus temperature plane shows novel reentrant behavior in the Mott transition due to the competition between Fermi-liquid formation and magnetic correlations under geometrical frustration. We demonstrate that the reentrant behavior is characteristic of the Mott transition with intermediate geometrical frustration and indeed consistent with recent experimental results of organic materials.
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.
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…
In the conventional ferromagnetic systems, topological magnon bands and thermal Hall effect are due to the Dzyaloshinskii-Moriya interaction (DMI). In principle, however, the DMI is either negligible or it is not allowed by symmetry in some quantum magnets. Therefore, we expect that topological magnon features will not be present in those systems. In addition, quantum magnets on the triangular-lattice are not expected to possess topological features as the DMI or spin-chirality cancels out due to equal and opposite contributions from adjacent triangles. Here, however, we predict that the isomo…
We investigate the role of electron correlation in the electronic structure of honeycomb lattice Li$_2$RuO$_3$ using photoemission spectroscopy and band structure calculations. Monoclinic Li$_2$RuO$_3$ having Ru network as honeycomb lattice undergoes magneto-structural transition at T$_c$ $\sim$ 540 K from high temperature phase $C2/m$ to low temperature dimerized phase $P2_1/m$. Room temperature valence band photoemission spectra reveal an insulating ground state with no intensity at Fermi level ($E_F$). Ru 4$d$ band extracted from high and low photon energy valence band photoemission spectra…
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…
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…
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 present the observation of an isostructural Mott insulator-metal transition in van-der-Waals honeycomb antiferromagnet V$_{0.9}$PS$_3$ through high-pressure x-ray diffraction and transport measurements. The MPX$_3$ family of magnetic van-der-Waals materials (M denotes a first row transition metal and X either S or Se) are currently the subject of broad and intense attention, but the vanadium compounds have until this point not been studied beyond their basic properties. We observe insulating variable-range-hopping type resistivity in V$_{0.9}$PS$_3$, with a gradual increase in effective dim…
Honeycomb iridates are thought to have strongly spin-anisotropic exchange interactions that could lead to an extraordinary state of matter known as the Kitaev quantum spin liquid. The realization of this state requires almost perfectly frustrated interactions between the magnetic Ir$^{4+}$ ions, but small imbalances in energy make other ordered states more favorable. Indeed, the closeness in energy of these ordered states is itself a signature of the intrinsic frustration in the system. In this work, we illustrate that small magnetic fields can be employed to drive the frustrated quantum magne…
Effects of electron many-body interactions amplify in an electronic system with a narrow bandwidth opening a way to exotic physics. A narrow band in a two-dimensional (2D) honeycomb lattice is particularly intriguing as combined with Dirac bands and topological properties but the material realization of a strongly interacting honeycomb lattice described by the Kane-Mele-Hubbard model has not been identified. Here we report a novel approach to realize a 2D honeycomb-lattice narrow-band system with strongly interacting 5$d$ electrons. We engineer a well-known triangular lattice 2D Mott insulator…
We study electric transport near the Mott metal-insulator transition in a triangular-lattice Hubbard model at half filling. We calculate optical conductivity $σ(ω)$ based on a cellular dynamical mean field theory including vertex corrections inside the cluster. Near the Mott critical end point, a Drude analysis in the metallic region suggests that the change in the Drude weight is important rather than that in the transport scattering rate for the Mott transition. In the insulating region, there emerges an "ingap" peak in $σ(ω)$ at low $ω$ near the Mott transition, and this smoothly connects t…
In quantum magnetism spin dimers are typically associated with spin-singlet states. To date, $triplet$ $dimerization$ has not been observed in any 3D or quasi-2D material. With this in mind we here discuss the electronic structure of the spin-orbit driven $5d^5$ Mott insulator Li$_2$IrO$_3$, a honeycomb-lattice system with two crystallographically inequivalent Ir-Ir bonds. From $ab$ $initio$ many-body calculations we find that, while both Heisenberg and Kitaev couplings are present, the magnetic interactions are dominated by a strong isotropic ferromagnetic exchange on only one set of bonds. T…
We investigate the classical phase diagram of the stuffed honeycomb Heisenberg lattice, which consists of a honeycomb lattice with a superimposed triangular lattice formed by sites at the center of each hexagon. This lattice encompasses and interpolates between the honeycomb, triangular and dice lattices, preserving the hexagonal symmetry while expanding the phase space for potential spin liquids. We use a combination of iterative minimization, classical Monte Carlo and analytical techniques to determine the complete ground state phase diagram. It is quite rich, with a variety of non-coplanar …
Electrons in artificial lattices enable explorations of the impact of repulsive Coulomb interactions in a tunable system. We have trapped two-dimensional electrons belonging to a gallium arsenide quantum well in a nanofabricated lattice with honeycomb geometry. We probe the excitation spectrum in a magnetic field identifying novel collective modes that emerge from the Coulomb interaction in the artificial lattice as predicted by the Mott-Hubbard model. These observations allow us to determine the Hubbard gap and suggest the existence of a novel Coulomb-driven ground state. This approach offers…
Spin liquid ground states are predicted to arise within several distinct scenarios in condensed matter physics. The observation of these disordered magnetic states is particularly pervasive amongst a class of materials known as frustrated magnets, in which the competition between various magnetic exchange interactions prevents the system from adopting long-range magnetic order at low temperatures. Spin liquids continue to be of great interest due to their exotic nature and the possibility that they may support fractionalised excitations, such as Majorana fermions. Systems that allow for such p…
We employ dynamical mean field theory (DMFT) with a Quantum Monte Carlo (QMC) atomic solver to investigate the finite temperature Mott transition in the Hubbard model with the nearest neighbor hopping on a triangular lattice at half-filling. We estimate the value of the critical interaction to be $U_c=12.0 \pm 0.5$ in units of the hopping amplitude $t$ through the evolution of the magnetic moment, spectral function, internal energy and specific heat as the interaction $U$ and temperature $T$ are varied. This work also presents a comparison between DMFT and finite size determinant Quantum Monte…
1T-TaS$_2$ is a charge-density-wave (CDW) compound with a Mott-insulating ground state. The metallic state obtained by doping, substitution or pulsed charge injection is characterized by an emergent CDW domain wall network, while single domain walls can be found in the pristine Mott state. Here we study whether and how the single walls become metallic. Tunneling spectroscopy reveals partial suppression of the Mott gap and the presence of in-gap states strongly localized at the domain-wall sites. Using the real-space dynamical mean field theory description of the strongly correlated quantum-par…
Based on dynamical cluster approximation (DCA) quantum Monte Carlo simulations, we study the interaction-driven Mott metal-insulator transition (MIT) in the half-filled Hubbard model on the anisotropic two-dimensional triangular lattice, where the degree of frustration is varied between the unfrustrated case and the fully frustrated, isotropic triangular lattice. Upon increasing the DCA cluster size, we analyze the evolution of the MIT phase boundary as a function of frustration in the phase diagram spanned by the interaction strength and temperature, and provide a quantitative description of …
We investigate the magnetic properties and Mott transition in the Hubbard model for weakly coupled chains on the anisotropic triangular lattice. Taking into account 120$^\circ$ Néel, and collinear orderings, the magnetic phase diagram is studied at zero temperature and half-filling by the variational cluster approximation. We found that when the on-site Coulomb repulsion $U$ is relatively large, nonmagnetic insulator, which is a candidate of the spin liquid state, is realized for wide range of the interchain hopping from quasi two-dimensional to almost one-dimensional regime. When the intercha…
Motivated by the recent discovery of a spin liquid phase for the Hubbard model on the honeycomb lattice at half-filling, we apply both perturbative and non-perturbative techniques to derive effective spin Hamiltonians describing the low-energy physics of the Mott-insulating phase of the system. Exact diagonalizations of the so-derived models on small clusters are performed, in order to assess the quality of the effective low-energy theory in the spin-liquid regime. We show that six-spin interactions on the elementary loop of the honeycomb lattice are the dominant sub-leading effective coupling…
We study Mott transition in the two-dimensional Hubbard model on an anisotropic triangular lattice. We use the Lanczos exact diagonalization of finite-size clusters up to eighteen sites, and calculate Drude weight, charge gap, double occupancy and spin structure factor. We average these physical quantities over twisted boundary conditions in order to reduce finite-size effects. We find a signature of the Mott transition in the dependence of the Drude weight and/or charge gap on the system size. We also examine the possibility of antiferromagnetic order from the spin structure factor. Combining…
In order to demonstrate that atomic Fermi gas is a good experimental reality in studying unsolved problems in frustrated interacting-spin systems, we numerically examine the Mott core state emerged by loading two-component atomic Fermi gases on triangular optical lattices. Consequently, we find that plateau like structures are observable in the Mott core polarization as a function of the population imbalance. These plateau states are caused by a flexibility that the surrounding metallic region absorbs the excess imbalance to keep the plateau states inside the Mott core. We also find spin patte…
We propose a novel quantum spin liquid state that can explain many of the intriguing experimental properties of the low-temperature phase of the organic spin liquid candidate materials. This state of paired fermionic spinons preserves all symmetries of the system, and it has a gapless excitation spectrum with quadratic bands that touch at momentum ~ k = 0. This quadratic band touching is protected by the symmetry of the system. Using variational Monte Carlo techniques, we show that this state has highly competitive energy in the triangular lattice Heisenberg model supplemented with a realistic…
Motivated by recent experiments on the triangular lattice Mott-Hubbard system kappa-(BEDT-TTF)2Cu2(CN)3, we develop a general formalism to investigate quantum spin liquid insulators adjacent to the Mott transition in Hubbard models. This formalism, dubbed the SU(2) slave-rotor formulation, is an extension of the SU(2) gauge theory of the Heisenberg model to the case of the Hubbard model. Furthermore, we propose the honeycomb lattice Hubbard model (at half-filling) as a candidate for a spin liquid ground state near the Mott transition; this is an appealing possibility, as this model can be stud…
We report the neutron scattering results on magnetic orderings and excitations in $\mathrm{Ba}_2\mathrm{CoTeO}_6$ composed of two almost isolated subsystems A and B, which are described as an $S\,{=}\,1/2$ triangular Heisenberg-like antiferromagnet and a frustrated honeycomb Ising-like antiferromagnet, respectively. Stripy ordering of subsystem B was confirmed below $T_{\rm N1}\,{=}\,12.0$ K, whereas sharp streaks were observed along $(1/3, 1/3, L)$ and $(2/3, 2/3, L)$ at 0.3 K (${\ll}\,T_{\rm N2}\,{=}\,3.0$ K). This indicates the two-dimensional nature of ordering in subsystem A. It was found…
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…
The Heisenberg-Kitaev (HK) model on the triangular lattice is conceptually interesting for its interplay of geometric and exchange frustration. HK models are also thought to capture the essential physics of the spin-orbital entanglement in effective $j=1/2$ Mott insulators studied in the context of various 5d transition metal oxides. Here we argue that the recently synthesized Ba$_3$IrTi$_2$O$_9$ is a prime candidate for a microscopic realization of the triangular HK model. We establish that an infinitesimal Kitaev exchange destabilizes the 120$^\circ$ order of the quantum Heisenberg model and…
We investigate the Hubbard model on the honeycomb lattice with intrinsic spin orbit interactions as a paradigm for two-dimensional topological band insulators in the presence of interactions. Applying a combination of Hartree-Fock theory, slave-rotor techniques, and topological arguments, we show that the topological band insulating phase persists up to quite strong interactions. Then we apply the slave-rotor mean-field theory and find a Mott transition at which the charge degrees of freedom become localized on the lattice sites. The spin degrees of freedom, however, are still described by the…
The ground state of Sn/Si(111) and Sn/Ge(111) surface $α$-phases is reexamined theoretically, based on $ab-initio$ calculations where correlations are approximately included through the orbital dependence of the Coulomb interaction (in the local density + Hubbard U approximation). The effect of correlations is to destabilize the vertical buckling in Sn/Ge(111) and to make the surface magnetic, with a metal-insulator transition for both systems. This signals the onset of a stable narrow gap Mott-Hubbard insulating state, in agreement with very recent experiments. Antiferromagnetic exchange is p…
Spin-liquid behavior was recently suggested experimentally in the moderately one-dimensional organic compound $κ$-H$_3$(Cat-EDT-TTF)$_2$. This compound can be modeled by the one-band Hubbard model on the anisotropic triangular lattice with $t^\prime/t \simeq 1.5$, where $t'$ is the minority hopping. It thus becomes important to extend previous studies, that were performed in the range $0 \leq t'/t \leq 1.2$, to find out whether there is a regime where Mott insulating behavior can be found without long-range magnetic order. To this end, we study the above model in the range $1.2 \leq t'/t \leq …
We report high resolution neutron scattering measurements on the triangular lattice Mott insulator Na$_x$CrO$_2$ ($x$=1) which has recently been shown to exhibit an unusually broad fluctuating crossover regime extending far below the onset of spin freezing ($T_c\sim$41K). Our results show that below some crossover temperature ($T\sim0.75T_c$) a small incommensuration develops which helps resolve the spin frustration and drives three-dimensional magnetic order supporting coherent spin wave modes. This incommensuration assisted dimensional crossover suggests that inter-layer frustration is respo…
1T-TaS$_2$ is a cluster Mott insulator on the triangular lattice with 13 Ta atoms forming a star of David cluster as the unit cell. We derive a two dimensional XXZ spin-1/2 model with four-spin ring exchange term to describe the effective low energy physics of a monolayer 1T-TaS$_2$, where the effective spin-1/2 degrees of freedom arises from the Kramers degenerate spin-orbital states on each star of David. A large scale density matrix renormalization group simulation is further performed on this effective model and we find a gapless spin liquid phase with spinon Fermi surface at moderate to l…
Magnetic phase diagram and Mott transition are studied in the Hubbard model on the anisotropic triangular lattice at zero temperature and half-filling by the variational cluster approximation, taking into account Néel, 120$^\circ$ Néel, and collinear orderings. Paramagnetic insulator (spin liquid) is realized above the metallic phase around the isotropic point. In general, this spin liquid state, continuously connected with the metallic state, changes to a magnetic state as the on-site Coulomb repulsion $U$ increases, but it persists up to large $U$ limit in a small window between 120$^\circ$ …
At strong repulsion, the triangular-lattice Hubbard model is described by $s=1/2$ spins with nearest-neighbor antiferromagnetic Heisenberg interactions and exhibits conventional 120$^\circ$ order. Using the infinite density matrix renormalization group and exact diagonalization, we study the effect of the additional four-spin interactions naturally generated from the underlying Mott-insulator physics of electrons as the repulsion decreases. Although these interactions have historically been connected with a gapless ground state with emergent spinon Fermi surface, we find that at physically rel…
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…
Interacting fermions on the half-filled honeycomb lattice with short-range repulsions have been suggested to host a variety of interesting many-body ground states, e.g., a topological Mott insulator. A number of recent studies of the spinless case in terms of exact diagonalization, the infinite density matrix renormalization group and the functional renormalization group, however, indicate a suppression of the topological Mott insulating phase in the whole range of interaction parameters. Here, we complement the previous studies by investigating the quantum many-body instabilities of the physi…
Phase transitions in the Hubbard model and ionic Hubbard model at half-filling on the honeycomb lattice are investigated in the strong coupling perturbation theory which corresponds to an expansion in powers of the hopping $t$ around the atomic limit. Within this formulation we find analytic expressions for the single-particle spectrum, whereby the calculation of the insulating gap is reduced to a simple root finding problem. This enables high precision determination of the insulating gap that does not require any extrapolation procedure. The critical value of Mott transition on the honeycomb …
