Exact Solution for Relativistic Two-Body Motion in Dilaton Gravity

We present an exact solution to the problem of the relativistic motion of 2 point masses in $(1+1)$ dimensional dilaton gravity. The motion of the bodies is governed entirely by their mutual gravitational influence, and the spacetime metric is likewise fully determined by their stress-energy. A Newtonian limit exists, and there is a static gravitational potential. Our solution gives the exact Hamiltonian to infinite order in the gravitational coupling constant.Comment: 6 pages, latex, 3 figure

Exact Charged 2-Body Motion and the Static Balance Condition in Lineal Gravity

We find an exact solution to the charged 2-body problem in $(1+1)$ dimensional lineal gravity which provides the first example of a relativistic system that generalizes the Majumdar-Papapetrou condition for static balance.Comment: latex,7 pages, 2 figure

A BCS-BEC crossover in the extended Falicov-Kimball model: Variational cluster approach

We study the spontaneous symmetry breaking of the excitonic insulator state induced by the Coulomb interaction $U$ in the two-dimensional extended Falicov-Kimball model. Using the variational cluster approximation (VCA) and Hartree-Fock approximation (HFA), we evaluate the order parameter, single-particle excitation gap, momentum distribution functions, coherence length of excitons, and single-particle and anomalous excitation spectra, as a function of $U$ at zero temperature. We find that in the weak-to-intermediate coupling regime, the Fermi surface plays an essential role and calculated results can be understood in close correspondence with the BCS theory, whereas in the strong-coupling regime, the Fermi surface plays no role and results are consistent with the picture of BEC. Moreover, we find that HFA works well both in the weak- and strong-coupling regime, and that the difference between the results of VCA and HFA mostly appears in the intermediate-coupling regime. The reason for this is discussed from a viewpoint of the self-energy. We thereby clarify the excitonic insulator state that typifies either a BCS condensate of electron-hole pairs (weak-coupling regime) or a Bose-Einstein condensate of preformed excitons (strong-coupling regime).Comment: 11 pages, 9 figure

Bogoliubov quasiparticle spectra of the effective d-wave model for cuprate superconductivity

An exact-diagonalization technique on finite-size clusters is used to study the ground state and excitation spectra of the two-dimensional effective fermion model, a fictious model of hole quasiparticles derived from numerical studies of the two-dimensional t-J model at low doping. We show that there is actually a reasonable range of parameter values where the $d_{x^2-y^2}$-wave pairing of holes occurs and the low-lying excitation can be described by the picture of Bogoliubov quasiparticles in the BCS pairing theory. The gap parameter of a size $\Delta_d\simeq 0.13|V|$ (where $V$ is the attractive interaction between holes) is estimated at low doping levels. The paired state gives way to the state of clustering of holes for some stronger attractions.Comment: 4 pages, RevTeX. Figures available upon request to [email protected]. To be published in Phys. Rev.

Doping dependent quasiparticle band structure in cuprate superconductors

We present an exact diagonalization study of the single particle spectral function in the so-called t-t'-t''-J model in 2D. As a key result, we find that unlike the `pure' t-J model, hole doping leads to a major reconstruction of the quasiparticle band structure near (pi,0): whereas for the undoped system the quasiparticle states near (pi,0) are deep below the top of the band at (pi/2,pi/2), hole doping shifts these states up to E_F, resulting in extended flat band regions close to E_F and around (pi,0). This strong doping-induced deformation can be directly compared to angle resolved photoemission results on Sr_2 Cu Cl_2 O_2, underdoped Bi2212 and optimally doped Bi2212. We propose the interplay of long range hopping and decreasing spin correlations as the mechanism of this deformation.Comment: 4 pages, Revtex, with 4 embedded eps figures. Hardcopies of figures (or the entire manuscript) can be obtained by e-mail request to [email protected]

Self-energy and Fermi surface of the 2-dimensional Hubbard model

We present an exact diagonalization study of the self-energy of the two-dimensional Hubbard model. To increase the range of available cluster sizes we use a corrected t-J model to compute approximate Greens functions for the Hubbard model. This allows to obtain spectra for clusters with 18 and 20 sites. The self-energy has several `bands' of poles with strong dispersion and extended incoherent continua with k-dependent intensity. We fit the self-energy by a minimal model and use this to extrapolate the cluster results to the infinite lattice. The resulting Fermi surface shows a transition from hole pockets in the underdoped regime to a large Fermi surface in the overdoped regime. We demonstrate that hole pockets can be completely consistent with the Luttinger theorem. Introduction of next-nearest neighbor hopping changes the self-energy stronlgy and the spectral function with nonvanishing next-nearest-neighbor hopping in the underdoped region is in good agreement with angle resolved photoelectron spectroscopy.Comment: 17 pages, 18 figure