Curve crossing in linear potential grids: the quasidegeneracy approximation

The quasidegeneracy approximation [V. A. Yurovsky, A. Ben-Reuven, P. S. Julienne, and Y. B. Band, J. Phys. B {\bf 32}, 1845 (1999)] is used here to evaluate transition amplitudes for the problem of curve crossing in linear potential grids involving two sets of parallel potentials. The approximation describes phenomena, such as counterintuitive transitions and saturation (incomplete population transfer), not predictable by the assumption of independent crossings. Also, a new kind of oscillations due to quantum interference (different from the well-known St\"uckelberg oscillations) is disclosed, and its nature discussed. The approximation can find applications in many fields of physics, where multistate curve crossing problems occur.Comment: LaTeX, 8 pages, 8 PostScript figures, uses REVTeX and psfig, submitted to Physical Review

Specific Heat of the 2D Hubbard Model

Quantum Monte Carlo results for the specific heat c of the two dimensional Hubbard model are presented. At half-filling it was observed that $c \sim T^2$ at very low temperatures. Two distinct features were also identified: a low temperature peak related to the spin degrees of freedom and a higher temperature broad peak related to the charge degrees of freedom. Away from half-filling the spin induced feature slowly disappears as a function of hole doping while the charge feature moves to lower temperature. A comparison with experimental results for the high temperature cuprates is discussed.Comment: 6 pages, RevTex, 11 figures embedded in the text, Submitted to Phys. Rev.

Nearly universal crossing point of the specific heat curves of Hubbard models

A nearly universal feature of the specific heat curves C(T,U) vs. T for different U of a general class of Hubbard models is observed. That is, the value C_+ of the specific heat curves at their high-temperature crossing point T_+ is almost independent of lattice structure and spatial dimension d, with C_+/k_B \approx 0.34. This surprising feature is explained within second order perturbation theory in U by identifying two small parameters controlling the value of C_+: the integral over the deviation of the density of states N(\epsilon) from a constant value, characterized by \delta N=\int d\epsilon |N(\epsilon)-1/2|, and the inverse dimension, 1/d.Comment: Revtex, 9 pages, 6 figure

Resonance Patterns of an Antidot Cluster: From Classical to Quantum Ballistics

We explain the experimentally observed Aharonov-Bohm (AB) resonance patterns of an antidot cluster by means of quantum and classical simulations and Feynman path integral theory. We demonstrate that the observed behavior of the AB period signals the crossover from a low B regime which can be understood in terms of electrons following classical orbits to an inherently quantum high B regime where this classical picture and semiclassical theories based on it do not apply.Comment: 5 pages revtex + 2 postscript figure

Insulator-Metal Transition in the One and Two-Dimensional Hubbard Models

We use Quantum Monte Carlo methods to determine $T=0$ Green functions, $G(\vec{r}, \omega)$, on lattices up to $16 \times 16$ for the 2D Hubbard model at $U/t =4$. For chemical potentials, $\mu$, within the Hubbard gap, $|\mu | < \mu_c$, and at {\it long} distances, $\vec{r}$, $G(\vec{r}, \omega = \mu) \sim e^{ -|\vec{r}|/\xi_l}$ with critical behavior: $\xi_l \sim | \mu - \mu_c |^{-\nu}$, $\nu = 0.26 \pm 0.05$. This result stands in agreement with the assumption of hyperscaling with correlation exponent $\nu = 1/4$ and dynamical exponent $z = 4$. In contrast, the generic band insulator as well as the metal-insulator transition in the 1D Hubbard model are characterized by $\nu = 1/2$ and $z = 2$.Comment: 9 pages (latex) and 5 postscript figures. Submitted for publication in Phys. Rev. Let

Fermionic R-Operator and Algebraic Structure of 1D Hubbard Model: Its application to quantum transfer matrix

The algebraic structure of the 1D Hubbard model is studied by means of the fermionic R-operator approach. This approach treats the fermion models directly in the framework of the quantum inverse scattering method. Compared with the graded approach, this approach has several advantages. First, the global properties of the Hamiltonian are naturally reflected in the algebraic properties of the fermionic R-operator. We want to note that this operator is a local operator acting on fermion Fock spaces. In particular, SO(4) symmetry and the invariance under the partial particle hole transformation are discussed. Second, we can construct a genuinely fermionic quantum transfer transfer matrix (QTM) in terms of the fermionic R-operator. Using the algebraic Bethe Ansatz for the Hubbard model, we diagonalize the fermionic QTM and discuss its properties.Comment: 22 pages, no 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