An extrapolation method for shell model calculations

We propose a new shell model method, combining the Lanczos digonalization and extrapolation method. This method can give accurate shell model energy from a series of shell model calculations with various truncation spaces, in a well-controlled manner. Its feasibility is demonstrated by taking the fp shell calculations.Comment: 4 pages, 5 figure

Thermodynamic Relations in Correlated Systems

Several useful thermodynamic relations are derived for metal-insulator transitions, as generalizations of the Clausius-Clapeyron and Eherenfest theorems. These relations hold in any spatial dimensions and at any temperatures. First, they relate several thermodynamic quantities to the slope of the metal-insulator phase boundary drawn in the plane of the chemical potential and the Coulomb interaction in the phase diagram of the Hubbard model. The relations impose constraints on the critical properties of the Mott transition. These thermodynamic relations are indeed confirmed to be satisfied in the cases of the one- and two-dimensional Hubbard models. One of these relations yields that at the continuous Mott transition with a diverging charge compressibility, the doublon susceptibility also diverges. The constraints on the shapes of the phase boundary containing a first-order metal-insulator transition at finite temperatures are clarified based on the thermodynamic relations. For example, the first-order phase boundary is parallel to the temperature axis asymptotically in the zero temperature limit. The applicability of the thermodynamic relations are not restricted only to the metal-insulator transition of the Hubbard model, but also hold in correlated systems with any types of phases in general. We demonstrate such examples in an extended Hubbard model with intersite Coulomb repulsion containing the charge order phase.Comment: 10 pages, 9 figure

What is Minimal Model of 3He Adsorbed on Graphite? -Importance of Density Fluctuations in 4/7 Registered Solid -

We show theoretically that the second layer of 3He adsorbed on graphite and solidified at 4/7 of the first-layer density is close to the fluid-solid boundary with substantial density fluctuations on the third layer. The solid shows a translational symmetry breaking as in charge-ordered insulators of electronic systems. We construct a minimal model beyond the multiple-exchange Heisenberg model. An unexpectedly large magnetic field required for the measured saturation of magnetization is well explained by the density fluctuations. The emergence of quantum spin liquid is understood from the same mechanism as in the Hubbard model and in \kappa-(ET)_2Cu_2(CN)_3 near the Mott transitions.Comment: 9 pages, 5 figure

On Deriving Nested Calculi for Intuitionistic Logics from Semantic Systems

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from its associated labelled calculus

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

Gossamer Superconductor, Mott Insulator, and Resonating Valence Bond State in Correlated Electron Systems

Gutzwiller variational method is applied to an effective two-dimensional Hubbard model to examine the recently proposed gossamer superconductor by Laughlin. The ground state at half filled electron density is a gossamer superconductor for smaller intra-site Coulomb repulsion U and a Mott insulator for larger U. The gossamer superconducting state is similar to the resonant valence bond superconducting state, except that the chemical potential is approximately pinned at the mid of the two Hubbard bands away from the half filled

Variational Monte Carlo Study of Electron Differentiation around Mott Transition

We study ground-state properties of the two-dimensional Hubbard model at half filling by improving variational Monte Carlo method and by implementing quantum-number projection and multi-variable optimization. The improved variational wave function enables a highly accurate description of the Mott transition and strong fluctuations in metals. We clarify how anomalous metals appear near the first-order Mott transition. The double occupancy stays nearly constant as a function of the on-site Coulomb interaction in the metallic phase near the Mott transition in agreement with the previous unbiased results. This unconventional metal at half filling is stabilized by a formation of ``electron-like pockets'' coexisting with an arc structure, which leads to a prominent differentiation of electrons in momentum space. An abrupt collapse of the ``pocket'' and ``arc'' drives the first-order Mott transition.Comment: 4 pages, 3 figure

Quantum Mott Transition and Multi-Furcating Criticality

Phenomenological theory of the Mott transition is presented. When the critical temperature of the Mott transition is much higher than the quantum degeneracy temperature, the transition is essentially described by the Ising universality class. Below the critical temperature, phase separation or first-order transition occurs. However, if the critical point is involved in the Fermi degeneracy region, a marginal quantum critical point appears at zero temperature. The originally single Mott critical point generates subsequent many unstable fixed points through various Fermi surface instabilities induced by the Mott criticality characterized by the diverging charge susceptibility or doublon susceptibility. This occurs in marginal quantum-critical region. Charge, magnetic and superconducting instabilitites compete severely under these critical charge fluctuations. The quantum Mott transition triggers multi-furcating criticality, which goes beyond the conventional concept of multicriticality in quantum phase transitions. Near the quantum Mott transition, the criticality generically drives growth of inhomogeneous structure in the momentum space with singular points of flat dispersion on the Fermi surface. The singular points determine the quantum dynamics of the Mott transition by the dynamical exponent $z=4$. We argue that many of filling-control Mott transitions are classified to this category. Recent numerical results as well as experimental results on strongly correlated systems including transition metal oxides, organic materials and $^3$He layer adsorbed on a substrate are consistently analyzed especially in two-dimensional systems.Comment: 28 pages including 2 figure

Spectral functions in itinerant electron systems with geometrical frustration

The Hubbard model with geometrical frustration is investigated in a metallic phase close to half-filling. We calculate the single particle spectral function for the triangular lattice within dynamical cluster approximation, which is further combined with non-crossing approximation and fluctuation exchange approximation to treat the resulting cluster Anderson model. It is shown that frustration due to non-local correlations suppresses short-range antiferromagnetic fluctuations and thereby assists the formation of heavy quasi-particles near half-filling.Comment: 4 pages, 5 eps figure

Exact diagonalization study of Mott transition in the Hubbard model on an anisotropic triangular lattice

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 these information, we propose a ground-state phase diagram which has a nonmagnetic insulating phase between a metallic phase and an insulating phase with antiferromagnetic order. Finally, we compare our results with those reported in the previous theoretical studies, and discuss the possibility of an unconventional insulating state.Comment: 10 pages, 11 figure