In the preprint cond-mat/0701060 we detected a factor two error in the coding of the Heisenberg term of the Hamiltonian. In the result the exchange term used in the paper was that of an anisotropic Heisenberg model with $J_x=J_y=J$ and $J_z=J/2$. Thus all results given for which J=0 was chosen, remain unchanged, whereas all results containing the exchange parameter remain true for the extended Hubbard model with anisotropic exchange. That model is of some interest by itself, due to the relation to the XXZ model. The differing results for isotropic exchange are given here.
We generalize the imaginary chemical potential quantum Monte Carlo (QMC) method proposed by Dagotto et al. [Phys. Rev. B 41, R811 (1990)] to systems without particle-hole symmetry. The generalized method is tested by comparing the results of the QMC simulations and exact diagonalization on small Hubbard molecules, such as tetrahedron and truncated tetrahedron. Results of the application of the method to the C$_{60}$ Hubbard molecule are discussed.
The Hubbard model extended by either nearest-neighbour Coulomb correlation and/or nearest neighbour Heisenberg exchange is solved analytically for a triangle and tetrahedron. All eigenvalues and eigenvectors are given as functions of the model parameters in a closed form. The groundstate crossings and degeneracies are discussed both for the canonical and grand-canonical energy levels. The grand canonical potential and the electron occupation of the related cluster gases were calculated for arbitrary values (attractive and repulsive) of the three interaction constants. In the pure Hubbard model…
We construct exact ground states of interacting electrons on triangle and diamond Hubbard chains. The construction requires (i) a rewriting of the Hamiltonian into positive semidefinite form, (ii) the construction of a many-electron ground state of this Hamiltonian, and (iii) the proof of the uniqueness of the ground state. This approach works in any dimension, requires no integrability of the model, and only demands sufficiently many microscopic parameters in the Hamiltonian which have to fulfill certain relations. The scheme is first employed to construct exact ground state for the diamond H…
We study the Hubbard model on the frustrated honeycomb lattice with nearest-neighbor $t_1$ and second nearest-neighbor hopping $t_2$, which is isomorphic to the bilayer triangle lattice, using the SU(2)-invariant slave boson theory. We show that the Coulomb interaction $U$ induces antiferromagnetic (AF) chiral spin-density wave ($χ$-SDW) order in a wide range of $κ=t_2/t_1$ where both the two-sublattice AF order at small $κ$ and the decoupled three-sublattice 120$^\circ$ order at large $κ$ are strongly frustrated, leading to three distinct phases with different anomalous Hall responses. We fin…
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…
We investigate heavy fermion behaviors in the vanadium spinel LiV_2O_4. We start from a three-orbital Hubbard model on the pyrochlore lattice and derive its low-energy effective Hamiltonian by an approach of real-space renormalization group type. One important tetrahedron configuration in the rochlore lattice has a three-fold orbital degeneracy and spin S=1, and correspondingly, the effective Hamiltonian has spin and orbital exchange interactions of Kugel-Khomskii type as well as correlated electron hoppings. Analyzing the effective Hamiltonian, we find that ferromagnetic double exchange proce…
Starting from the archetypical geometrically frustrated magnetic objects -- equilateral triangle and tetrahedron -- we consider an imaginary object: a multidimensional tetrahedron with spins $1/2$ in the each vertex and equal Heisenberg magnetic exchange along each edge. Many-particle case is obtained by setting dimensionality $d$ to high numbers, hence providing likely the most geometrically frustrated magnetic system ever possible. This problem has an exact solution for each $d$, obtained by simple student-level approach. As a result, this imaginary object clearly demonstrates at $d\to{}\inf…
Motivated by recent experiment on the Na$_4$Ir$_3$O$_8$ compound we study the Hubbard model on the "hyper-kagome lattice", which forms a three-dimensional network of corner sharing triangles, using dynamical cluster approximation (DCA) method with $N_c$=12 combined with the continuous-time quantum Monte Carlo (CT QMC) method. The system undergoes a Mott transition if the Hubbard interaction $U/W$ ($W$ is the bandwidth) exceeds the value of 1.2 for $T$=0.1 and displays reentrant behavior due to competition between the magnetic correlation and the kinetic energy of electrons due to the geometric…
We study the phase diagram of the extended Hubbard model on the kagome lattice at 1/3 filling. By combining a configuration interaction approach to an unrestricted Hartree-Fock, we construct an effective hamiltonian which takes the correlations back on top of the mean-field solution. We obtain a rich phase diagram with, in particular, the presence of two original phases. The first one consists of polarized droplets of metal standing on the hexagons of the lattice, and an enlarged kagome charge order, inversely polarized, on the remaining sites. The second, obeying a local ice-rule type constra…
We consider the antiferromagnetic Heisenberg and the repulsive Hubbard model on two $N$-site one-dimensional lattices, which support dispersionless one-particle states corresponding to localized states on triangular trapping cells. We calculate the degeneracy of the ground states in the subspaces with $n\le n_{\max}$, $n_{\max}\propto N$ magnons or electrons as well as the contribution of these states (independent localized states) to thermodynamic quantities. Moreover, we discuss another class of low-lying eigenstates (so-called interacting localized states) and calculate their contribution t…
We theoretically study a generalized Hubbard model on moiré superlattices of twisted bilayers, and find very rich filling-factor-dependent quantum phase diagrams tuned by interaction strength and twist angle. Strong long-range Coulomb interaction in the moiré-Hubbard model induces Wigner crystals at a series of fractional filling factors. The effective lattice of the Wigner crystal is controlled by the filling factor, and can be triangle, rectangle, honeycomb, kagome, etc, providing a single platform to realize many different spin models on various lattices by simply tuning carrier density. In…
The spontaneously broken of translational symmetry is usually due to the competition between local interactions and long-range interactions. However, in this paper, we show how a crystalline order can be generated by the competition between local interaction and long-range correlation by frustration. Here we propose a positive hopping Bose Hubbard model on triangle lattices with a pair creation term which comes from frustrated linked cavity arrays with degenerate quantum gases in them. We find by increasing the strength of pair creation term against local interaction strength, two kinds of den…
We study the effects of a periodically varying electric field on the Hubbard model at half-filling on a triangular lattice. The electric field is incorporated through the phase of the nearest-neighbor hopping amplitude via the Peierls prescription. When the on-site interaction $U$ is much larger than the hopping, the effective Hamiltonian $H_{eff}$ describing the spin sector can be found using a Floquet perturbation theory. To third order in the hopping, $H_{eff}$ is found to have the form of a Heisenberg antiferromagnet with three different nearest-neighbor couplings $(J_α,J_β,J_γ)$ on bonds …
We demonstrate that at a filling of $n=1.5$, an hexatic insulating state obtains in the extended Hubbard model on a triangular lattice. Composed of two tetragonal sublattices with fillings of $n=1$ and $n=2$, the insulating state is charge ordered and possesses an antiferromagnetic superlattice with dimension $a\times\sqrt{3}$. Two distinct energy scales arise in our model, a charge gap for the insulator and the effective exchange interaction in the antiferromagnet. Our model is capable of explaining both qualitatively and quantitatively the Hall coefficient including the sign change, the temp…
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. Further, we find a quantum phase transition between two different density ordered superfluids, which is beyond the Landau-Ginzburg paradigm. Across this transition, a U(1) symmetry is emergent, while the symmetry in each density…
A derivation of the t-J model of a highly-correlated solid is given starting from the general many-electron Hamiltonian with account of the non-orthogonality of atomic wave functions. Asymmetry of the Hubbard subbands (i.e. of ``electron'' and ``hole''cases) for a nearly half-filled bare band is demonstrated. The non-orthogonality corrections are shown to lead to occurrence of indirect antiferromagnetic exchange interaction even in the limit of the infinite on-site Coulomb repulsion. Consequences of this treatment for the magnetism formation in narrow energy bands are discussed. Peculiarities …
We study the ground-state magnetism of the half-filled Hubbard model on the anisotropic triangular lattice, where two out of three bonds have hopping $t$ and the third one has $t^\prime$ in a unit triangle. Working in a spin-rotating frame and using the density matrix renormalization group method as an impurity solver, we provide a proper description of incommensurate magnetizations at zero temperature in the framework of the dynamical mean-field theory (DMFT). It is shown that the incommensurate spiral magnetic order for $t^\prime/t\gtrsim 0.7$ survives the dynamical fluctuations of itinerant…
