Doublon–holon-binding mechanism of Mott transition in 2D Hubbard model

The mechanism of nonmagnetic Mott transitions in the Hubbard model on the square lattice is studied, using a variational Monte Carlo method. A simple doublon (D)–holon (H) binding mechanism a previous study proposed [J. Phys. Soc. Jpn. 75 (2006) 114706] has to be modified, because even a wave function with completely bound D–H pairs brings about a Mott transition at a finite correlation strength. By introducing two characteristic lengths, D–H pair binding length, ξ_DH, and minimum inter-doublon distance, ξ_DD, we can properly describe the physics of Mott transitions, and determine the critical point by ξ_DD ～ ξ_DH. This concept seems universal, because it is valid not only for newly introduced wave functions with long-range D–H and D–D (H–H) correlation factors discussed here, but for a wide range of wave functions with D–H binding factors.     

Low-energy singlets in the Heisenberg antiferromagnet on the kagomé lattice

The spin-1/2 Heisenberg antiferromagnet on the kagomé lattice, is mapped by contractor renormalization to a spin-pseudospin Hamiltonian on the triangular superlattice. Variationally, we find a ground state with columnar dimer order. Dimer orientation fluctuations are described by an effective O(2) model at energies above an exponentially suppressed clock mass scale. Our results explain the large density of low-energy singlets observed numerically, and the nonmagnetic T2 specific heat observed experimentally.     

Exact ground states of the extended Hubbard model on the Kagomé lattice

We discuss the exact plaquette-ordered ground states of the generalized Hubbard model on the Kagomé lattice for several fillings, by constructing the Hamiltonian as a sum of products of projection operators for up and down spin sectors. The obtained exact ground states are interpreted as Néel ordered states on the bond-located electrons. We determine several parameter regions of the exact ground states, and calculate the entanglement entropy. We examine the above results by numerical calculations based on exact diagonalization and density-matrix renormalization group methods.     

Mott insulator-density ordered superfluid transition and ‘shamrock transition’ in a frustrated triangle lattice

Density order is usually a consequence of the competition between long-range and short-range interactions. Here we report a density ordered superfluid emergent from a homogeneous Mott insulator due to the competition between frustrations and local interactions. This transition is found in a Bose–Hubbard model on a frustrated triangle lattice with an extra pairing term. Furthermore, we find a quantum phase transition between two different density ordered superfluids, which is beyond the Landau–Gi...     

The Berezinskii-Kosterlitz-Thouless transition and correlations in the XY kagomé antiferromagnet

The problem of the Berezinskii-Kosterlitz-Thouless transition in the highly frustrated XY kagomé antiferromagnet is solved. The transition temperature is found. It is shown that the spin correlation function exponentially decays with distance even in the low-temperature phase, in contrast to the order parameter correlation function, which decays algebraically with distance.     

Quantum magnetism in the paratacamite family: towards an ideal kagomé lattice

We report muon spin rotation measurements on the S=1/2 (Cu2+) paratacamite ZnxCu4-x(OH)6Cl2 family. Despite a Weiss temperature of approximately -300 K, the x=1 compound is found to have no transition to a magnetic frozen state down to 50 mK as theoretically expected for the kagomé Heisenberg antiferromagnet. We find that the limit between a dynamical and a partly frozen ground state occurs around x=0.5. For x=1, we discuss the relevance to a singlet picture.     

Bogoliubov excitations in a Bose–Hubbard model on a hyperhoneycomb lattice

We study the topological properties of Bogoliubov excitation modes in a Bose–Hubbard model of three-dimensional(3 D) hyperhoneycomb lattices. For the non-interacting case, there exist nodal loop excitations in the Bloch bands. As the on-site repulsive interaction increases, the system is first driven into the superfluid phase and then into the Mott-insulator phase. In both phases, the excitation bands exhibit robust nodal-loop structures and bosonic surface states. From a topology point of view, these nodal-loop excitation modes may be viewed as a permanent fingerprint left in the Bloch bands.     

Atomic Fermi gas in the trimerized kagomé lattice at 2/3 filling

We study low temperature properties of a spinless interacting Fermi gas in the trimerized kagomé lattice. The case of two fermions per trimer is described by a quantum spin 1/2 model on the triangular lattice with couplings depending on the bond directions. Using exact diagonalizations we show that the system exhibits nonstandard properties of a quantum spin-liquid crystal, combining a planar antiferromagnetic order with an exceptionally large number of low-energy excitations.     

Spin-liquid state for two-dimensional Heisenberg antiferromagnets on a kagomé lattice

The magnetic properties of the spin liquid state of the antiferromagnetic Heisenberg model on the kagomé lattice are investigated within the self-consistent mean-field theory. The results show that the spin liquid ground-state energy per site is , which is in very good agreement with the best numerical estimates. The spin structure factor and spin susceptibility are also discussed. Received 1 December 1998 and Received in final form 12 April 1999     

Anisotropic Hubbard model on a triangular lattice — spin dynamics in HoMnO3

The recent neutron scattering data for spin-wave dispersion in HoMnO₃ are well-described by an anisotropic Hubbard model on a triangular lattice with a planar (XY) spin anisotropy. Best fit indicates that magnetic excitations in HoMnO₃ correspond to the strong-coupling limit U/t >∼ 15, with planar exchange energy J = 4t ² /U ≃ 2.5 meV and planar anisotropy ΔU ≃ 0.35 meV.      

Field-induced transitions in a kagomé antiferromagnet

The thermal order by disorder effect in magnetic field is studied for a classical Heisenberg antiferromagnet on the Kagomé lattice. Using analytical arguments we predict a unique H- T phase diagram for this strongly frustrated magnet: states with a coplanar and a uniaxial triatic order parameter, respectively, at low and high magnetic fields and an incompressible collinear spin-liquid state at one-third of the saturation field. We also present the Monte Carlo data which confirm the existence of these phases.     

Muon spin relaxation measurements in kagomé lattice system SrCr8Ga4O19

Dynamical spin fluctuations in SrCr_8–xGa_4+xO₁₉ a frustrated spin system on a kagomé lattice, is examined by the longitudinal field muon spin relaxation technique. This system shows a spin-glass (SG)-like cusp in the susceptibility atT _g=3.5(2) K. The slowing down of Cr spin fluctuations is found to occur over a very wide temperature rangeT _g<T<30T _g. AsT/T _g 0 these fluctuations remain without static polarization (order parameter). Such strong fluctuations belowT _g have not been observed before in a conventional SG system.     

Magnetic correlations in the Hubbard model on triangular and Kagomé lattices

In order to study the magnetic properties of frustrated metallic systems, we present, for the first time, quantum Monte Carlo data on the magnetic susceptibility of the Hubbard model on triangular and kagomé lattices. We show that the underlying lattice structure determines the nature and the doping dependence of the magnetic fluctuations. In particular, in the doped kagomé case we find strong short-range magnetic correlations, which makes the metallic kagomé systems a promising field for studies of superconductivity.     

Quantum coherence and ground-state phase transition in a four-chain Bose–Hubbard model

We study the quantum coherence and ground-state phase transition of a four-chain Bose–Hubbard model with the long-range interaction. In a special four-chain Bose–Hubbard model,i.e., each chain only has one optical potential, four types of the ground-state phases are discovered. The effects of the disorder, the on-site interaction and the long-range interaction on the quantum coherence are studied. For the system without the long-range interaction, the quantum coherence changes from one periodic oscillation to two periodic oscillations as the onsite interaction increases. By considering the long-range interaction, the quantum coherence goes back to one periodic oscillation again. The on-site interaction itself suppresses the quantum coherence, both the on-site interaction and long-range interaction together enhance the quantum coherence with the weak disorder. If the disorder strength is increased beyond a critical value,they start to suppress the quantum coherence. In a regular four-chain Bose–Hubbard model, i.e.,each chain has many optical potentials, the ground-state phase transitions are obtained by using the cluster Gutzwiller mean-field method. Exotic ground-state phases are found, i.e., superfluid phase, integer Mott insulator phase, supersolid phase and loophole insulator phase. The combination of the loophole insulator phase and the supersolid phase expands the lobes with the half-integer filling per site for the small ratio β = t_■/t_⊥.     

Hund’s coupling and the metal-insulator transition in the two-band Hubbard model

The Mott-Hubbard metal-insulator transition is investigated in a two-band Hubbard model within dynamical mean-field theory. To this end, we use a suitable extension of Wilsons numerical renormalization group for the solution of the effective two-band single-impurity Anderson model. This method is non-perturbative and, in particular, allows to take into account the full exchange part of the Hunds rule coupling between the two orbitals. We discuss in detail the influence of the various Coulomb interactions on thermodynamic and dynamic properties, for both the impurity and the lattice model. The exchange part of the Hunds rule coupling turns out to play an important role for the physics of the two-band Hubbard model and for the nature of the Mott-transition.     

Topological quantum phase transitions and topological flat bands on the kagomé lattice

We investigate the topological properties of the tight-binding electrons on the two-dimensional kagomé lattice with two kinds of short-range hopping integral and two kinds of staggered magnetic flux. Considering the nearest-neighbor hopping (t(1)) with the staggered flux parameter φ(1) and the next nearest-neighbor hopping (t(2)) with the staggered flux parameter φ(2), we demonstrate a series of topological quantum phase transitions and find some topological bands with high Chern numbers, when tuning one parameter (t(2) or φ(2)) while the others are fixed. We have also found that, in some parameter regions, the system exhibits interesting topological flat bands with Chern number C =± 1 and a large gap above them, and the flatness ratio can reach a high value of about 170.