Algebraic Bethe ansatz for the one-dimensional Hubbard model with chemical potential

The integrability and the algebraic Bethe ansatz approach for the one-dimensional (1D) Hubbard model with chemical potential are studied in the framework of the quantum inverse scattering method. We also investigate the hidden local gauge invariance for the model. It is found that the R-matrix only permits Abelian $\text{U(1) ⋇}{}_{\mathrm{s}}\text{U(1)}$ gauge transformations, and it is shown that the energy spectrum is gauge invariant whereas the eigenvectors and the Bethe ansatz equations are explicitly gauge dependent.     

Second order self-energy of the two-dimensional Hubbard model

The self-energy Σ(k; ω) of the 2D Hubbard model on the square lattice is calculated numerically in second order perturbation theory. In the limit of small frequencies the imaginary part of Σ(k; ω) is also obtained analytically. We find that at half filling ImΣ(k; ω) ～ ω for k on the Fermi surface, with a logarithmically divergent prefactor close to the corners k = (0,±π) and (±π,0) in agreement with the numerical results.     

Doping dependence of charge order in electron-doped cuprate superconductors

Abstract

In the recent studies of the unconventional physics in cuprate superconductors, one of the central issues is the interplay between charge order and superconductivity. Here the mechanism of the charge-order formation in the electron-doped cuprate superconductors is investigated based on the t-J model. The experimentally observed momentum dependence of the electron quasiparticle scattering rate is qualitatively reproduced, where the scattering rate is highly anisotropic in momentum space, and is intriguingly related to the charge-order gap. Although the scattering strength appears to be weakest at the hot spots, the scattering in the antinodal region is stronger than that in the nodal region, which leads to the original electron Fermi surface is broken up into the Fermi pockets and their coexistence with the Fermi arcs located around the nodal region. In particular, this electron Fermi surface instability drives the charge-order correlation, with the charge-order wave vector that matches well with the wave vector connecting the hot spots, as the charge-order correlation in the hole-doped counterparts. However, in a striking contrast to the hole-doped case, the charge-order wave vector in the electron-doped side increases in magnitude with the electron doping. The theory also shows the existence of a quantitative link between the single-electron fermiology and the collective response of the electron density.     

Variational tests of current order parameters in the Hubbard model

Variational tests are performed for current order parameters as probable sources of the pseudogap normal state of cuprates. The calculations are carried out based on the states with correlations of the valence bond type whose formation can induce in principle both the superconducting order of the d symmetry and current phases. It is shown for the t-t′-U Hubbard models with a large value of U(～8t) and the Hubbard splitting of the conduction band that (1) phases of alternating charge and longitudinal spin currents cannot be realized and (2) transverse spin currents are not compatible with the superconducting order and they could exist against the normal-state background only within a very narrow doping region near the optimal one. This region does not correspond to the region of existence of a pseudogap in cuprates, which refutes the above-mentioned hypothesis of the pseudogap origin. The requirements to the parameters of models for which the consideration of correlations of the valence bond type yields a reasonable phase curve. The existence of current phases in the t-t′-U-V Hubbard models with a strong interaction (V>0.25t) of particles in neighboring sites is predicted when the d-superconductivity is completely suppressed.     

Evidence for energy dependence in the isospin dependent part of the nuclear optical model potential

Angular distributions and the excitation function of the total cross section for the ²⁰⁸Pb(p, n) charge exchange reaction are fitted with DWBA calculations. Isospin potentials which have the relative real volume and surface imaginary strengths found in the optical model studies of Becchetti and Greenlees provide adequate fits to the angular distributions. The excitation function indicates a strong energy dependence in the strength of the isospin potential.     

Impact parameter dependence of electronic energy loss

Energy-loss moments of the electronic energy loss are calculated as functions of impact parameter for protons of 1 to 7 MeV incident upon Be, Al, Cu, Ag, and Ta targets. The Lindhard dielectric-function formalism is used, in the local-density approximation. The target-atom electron densities are Lenz-Jensen, and the projectile is a point charge. The moments are fitted by a simple algebraic function, and the energy and Z₂ dependence of the parameters of this function are given.     

Temperature dependence of the relaxation time of the superconducting order parameter

We have measured the temperature dependences of the relaxation time of the superconducting order parameter and of the equilibrium energy gap close to the transition temperature in very clean films of aluminum. The results are only consistent with the temperature and energy gap dependence predicted by Schmid and Schön. We also show that the magnitude and mean free path dependence of the electron inelastic collision time is in good agreement with calculations.     

Nodal quasiparticles and the onset of spin-density-wave order in cuprate superconductors

We present a theory for the onset of spin-density-wave order in the superconducting ground state of the cuprates. We compute the scaling dimensions of allowed perturbations of a "relativistic" fixed point with O4 x O(3) symmetry, including those associated with the fermionic nodal Bogoliubov quasiparticles. Analyses of up to six loops show that all perturbations with square lattice symmetry are likely irrelevant. We demonstrate that the fermion spectral functions are primarily damped by the coupling to fluctuations of a composite field with Ising nematic order. A number of other experimental implications are also discussed.     

Ground-state energy of the Hubbard model in the BCS approximation

In the paper it is shown that it is possible to apply the BCS theory to the Hubbard model with positiveU for a half-filled band. A calculation of the ground-state energy of the model is presented.