Quantum Phase Transitions to Charge Order and Wigner Crystal Under Interplay of Lattice Commensurability and Long-Range Coulomb Interaction

Relationship among Wigner crystal, charge order and Mott insulator is studied by the path-integral renormalization group method for two-dimensional lattices with long-range Coulomb interaction. In contrast to Hartree-Fock results, the solid stability drastically increases with lattice commensurability. The transition to liquid occurs at the electron gas parameter $r_s \sim 2$ for the filling $n=1/2$ showing large reduction from $r_s \sim 35$ in the continuum limit. Correct account of quantum fluctuations are crucial to understand charge-order stability generally observed only at simple fractional fillings and nature of quantum liquids away from them.Comment: 4 pages including 7 figure

Quantum-number projection in the path-integral renormalization group method

We present a quantum-number projection technique which enables us to exactly treat spin, momentum and other symmetries embedded in the Hubbard model. By combining this projection technique, we extend the path-integral renormalization group method to improve the efficiency of numerical computations. By taking numerical calculations for the standard Hubbard model and the Hubbard model with next nearest neighbor transfer, we show that the present extended method can extremely enhance numerical accuracy and that it can handle excited states, in addition to the ground state.Comment: 11 pages, 7 figures, submitted to Phys. Rev.

Suppressed Coherence due to Orbital Correlations in the Ferromagnetically Ordered Metallic Phase of Mn Compounds

Small Drude weight $D$ together with small specific heat coefficient $\gamma$ observed in the ferromagnetic phase of R$_{1-x}$A$_x$MnO$_3$ (R=La, Pr, Nd, Sm; A=Ca, Sr, Ba) are analyzed in terms of a proximity effect of the Mott insulator. The scaling theory for the metal-insulator transition with the critical enhancement of orbital correlations toward the staggered ordering of two $e_g$ orbitals such as $3x^2-r^2$ and $3y^2-r^2$ symmetries may lead to the critical exponents of $D \propto \delta^{u}$ and $\gamma \propto \delta^v$ with $u=3/2$ and $v=0$. The result agrees with the experimental indications.Comment: 4 pages LaTeX using jpsj.sty. To appear in J. Phys. Soc. Jpn. 67(1998)No.

Finite-Temperature Mott Transition in the Two-Dimensional Hubbard Model

Mott transitions are studied in the two-dimensional Hubbard model by a non-perturbative theory of correlator projection that systematically includes spatial correlations into the dynamical mean-field approximation. Introducing a nonzero second-neighbor transfer, a first-order Mott transition appears at finite temperatures and ends at a critical point or curve.Comment: 2 pages, to appear in J. Mag. Mag. Mat. as proceedings of the International Conference on Magnetism 200

Theory of Electron Differentiation, Flat Dispersion and Pseudogap Phenomena

Aspects of electron critical differentiation are clarified in the proximity of the Mott insulator. The flattening of the quasiparticle dispersion appears around momenta $(\pi,0)$ and $(0,\pi)$ on square lattices and determines the criticality of the metal-insulator transition with the suppressed coherence in that momentum region of quasiparticles. Such coherence suppression at the same time causes an instability to the superconducting state if a proper incoherent process is retained. The d-wave pairing interaction is generated from such retained processes without disturbance from the coherent single-particle excitations. Pseudogap phenomena widely observed in the underdoped cuprates are then naturally understood from the mode-mode coupling of d-wave superconducting(dSC) fluctuations with antiferromagnetic ones. When we assume the existence of a strong d-wave pairing force repulsively competing with antiferromagnetic(AFM) fluctuations under the formation of flat and damped single-particle dispersion, we reproduce basic properties of the pseudogap seen in the magnetic resonance, neutron scattering, angle resolved photoemission and tunneling measurements in the cuprates.Comment: 9 pages including 2 figures, to appear in J. Phys. Chem. Solid

Drude Weight of the Two-Dimensional Hubbard Model -- Reexamination of Finite-Size Effect in Exact Diagonalization Study --

The Drude weight of the Hubbard model on the two-dimensional square lattice is studied by the exact diagonalizations applied to clusters up to 20 sites. We carefully examine finite-size effects by consideration of the appropriate shapes of clusters and the appropriate boundary condition beyond the imitation of employing only the simple periodic boundary condition. We successfully capture the behavior of the Drude weight that is proportional to the squared hole doping concentration. Our present result gives a consistent understanding of the transition between the Mott insulator and doped metals. We also find, in the frequency dependence of the optical conductivity, that the mid-gap incoherent part emerges more quickly than the coherent part and rather insensitive to the doping concentration in accordance with the scaling of the Drude weight.Comment: 9 pages with 10 figures and 1 table. accepted in J. Phys. Soc. Jp

Superconductivity from Flat Dispersion Designed in Doped Mott Insulators

Routes to enhance superconducting instability are explored for doped Mott insulators. With the help of insights for criticalities of metal-insulator transitions, geometrical design of lattice structure is proposed to control the instability. A guideline is to explicitly make flat band dispersions near the Fermi level without suppressing two-particle channels. In a one-dimensional model, numerical studies show that our prescription with finite-ranged hoppings realizes large enhancement of spin-gap and pairing dominant regions. We also propose several multi-band systems, where the pairing is driven by intersite Coulomb repulsion.Comment: 4 pages, to be published in Phys. Rev. Let

Superconductivity Driven by the Interband Coulomb Interaction and Implications for the Superconducting Mechanism of MgB2

Superconducting mechanism mediated by interband exchange Coulomb repulsion is examined in an extended two-band Hubbard models with a wide band crossing the Fermi level and coexisting with a narrower band located at moderately lower energy. We apply newly developed path-integral renormalization group method to reliably calculate pairing correlations. The correlation shows marked enhancement at moderate amplitudes of the exchange Coulomb repulsion taken smaller than the on-site repulsion for the narrower band. The pairing symmetry is s-wave while it has unconventional phases with the opposite sign between the order parameters on the two bands, in agreement with the mean-field prediction. Since the band structure of recently discovered superconductor MgB$_2$ shares basic similarities with our model, we propose that the present results provide a relevant clue for the understanding of the superconducting mechanism in MgB$_2$ as well as in this class of multi-band materials with good metallic conduction in the normal state.Comment: 4pages, 2figure

Fate of Quasiparticle at Mott Transition and Interplay with Lifshitz Transition Studied by Correlator Projection Method

Filling-control metal-insulator transition on the two-dimensional Hubbard model is investigated by using the correlator projection method, which takes into account momentum dependence of the free energy beyond the dynamical mean-field theory. The phase diagram of metals and Mott insulators is analyzed. Lifshitz transitions occur simultaneously with metal-insulator transitions at large Coulomb repulsion. On the other hand, they are separated each other for lower Coulomb repulsion, where the phase sandwiched by the Lifshitz and metal-insulator transitions appears to show violation of the Luttinger sum rule. Through the metal-insulator transition, quasiparticles retain nonzero renormalization factor and finite quasi-particle weight in the both sides of the transition. This supports that the metal-insulator transition is caused not by the vanishing renormalization factor but by the relative shift of the Fermi level into the Mott gap away from the quasiparticle band, in sharp contrast with the original dynamical mean-field theory. Charge compressibility diverges at the critical end point of the first-order Lifshitz transition at finite temperatures. The origin of the divergence is ascribed to singular momentum dependence of the quasiparticle dispersion.Comment: 24 pages including 10 figure