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

Destruction of Superconductivity by Impurities in the Attractive Hubbard Model

We study the effect of U=0 impurities on the superconducting and thermodynamic properties of the attractive Hubbard model on a square lattice. Removal of the interaction on a critical fraction of $f_{\rm crit} \approx 0.30$ of the sites results in the destruction of off-diagonal long range order in the ground state. This critical fraction is roughly independent of filling in the range $0.75 < \rho < 1.00$, although our data suggest that $f_{\rm crit}$ might be somewhat larger below half-filling than at $\rho=1$. We also find that the two peak structure in the specific heat is present at $f$ both below and above the value which destroys long range pairing order. It is expected that the high $T$ peak associated with local pair formation should be robust, but apparently local pairing fluctuations are sufficient to generate a low temperature peak

Counterintuitive transitions in the multistate Landau-Zener problem with linear level crossings

We generalize the Brundobler-Elser hypothesis in the multistate Landau-Zener problem to the case when instead of a state with the highest slope of the diabatic energy level there is a band of states with an arbitrary number of parallel levels having the same slope. We argue that the probabilities of counterintuitive transitions among such states are exactly zero.Comment: 9 pages, 5 figure

Electrical Conductivity of Fermi Liquids. I. Many-body Effect on the Drude Weight

On the basis of the Fermi liquid theory, we investigate the many-body effect on the Drude weight. In a lattice system, the Drude weight $D$ is modified by electron-electron interaction due to Umklapp processes, while it is not renormalized in a Galilean invariant system. This is explained by showing that the effective mass $m'$ for $D\propto n/m'$ is defined through the current, not velocity, of quasiparticle. It is shown that the inequality $D>0$ is required for the stability against the uniform shift of the Fermi surface. The result of perturbation theory applied for the Hubbard model indicates that $D$ as a function of the density $n$ is qualitatively modified around half filling $n\sim 1$ by Umklapp processes.Comment: 20 pages, 2 figures; J. Phys. Soc. Jpn. Vol.67, No.

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

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

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

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