Nearest-neighbour Attraction Stabilizes Staggered Currents in the 2D Hubbard Model

Using a strong-coupling approach, we show that staggered current vorticity does not obtain in the repulsive 2D Hubbard model for large on-site Coulomb interactions, as in the case of the copper oxide superconductors. This trend also persists even when nearest-neighbour repulsions are present. However, staggered flux ordering emerges {\bf only} when attractive nearest-neighbour Coulomb interactions are included. Such ordering opens a gap along the $(\pi,0)-(0,\pi)$ direction and persists over a reasonable range of doping.Comment: 5 pages with 5 .eps files (Typos in text are corrected

RKKY interaction in the nearly-nested Fermi liquid

We present the results of analytical evaluation of the indirect RKKY interaction in a layered metal with nearly nested (almost squared) Fermi surface. The final expressions are obtained in closed form as a combination of Bessel functions. We discuss the notion of the ``2k_F'' oscillations and show that they occur as the far asymptote of our expressions. We show the existence of the intermediate asymptote of the interaction which is of the sign-reversal antiferromagnetic type and is the only term surviving in the limit of exact nesting. A good accordance of our analytical formulas with numerical findings is demonstrated until the interatomic distances. The obtained expressions for the Green's functions extend the previous analytical results into the region of intermediate distances as well.Comment: 9 pages, REVTEX, 3 .eps figures, to appear in PRB 1 Oct 199

Decoherence of electron spin qubits in Si-based quantum computers

Direct phonon spin-lattice relaxation of an electron qubit bound by a donor impurity or quantum dot in SiGe heterostructures is investigated. The aim is to evaluate the importance of decoherence from this mechanism in several important solid-state quantum computer designs operating at low temperatures. We calculate the relaxation rate $1/T_1$ as a function of [100] uniaxial strain, temperature, magnetic field, and silicon/germanium content for Si:P bound electrons. The quantum dot potential is much smoother, leading to smaller splittings of the valley degeneracies. We have estimated these splittings in order to obtain upper bounds for the relaxation rate. In general, we find that the relaxation rate is strongly decreased by uniaxial compressive strain in a SiGe-Si-SiGe quantum well, making this strain an important positive design feature. Ge in high concentrations (particularly over 85%) increases the rate, making Si-rich materials preferable. We conclude that SiGe bound electron qubits must meet certain conditions to minimize decoherence but that spin-phonon relaxation does not rule out the solid-state implementation of error-tolerant quantum computing.Comment: 8 figures. To appear in PRB-July 2002. Revisions include: some references added/corrected, several typos fixed, a few things clarified. Nothing dramati

Electronic dynamic Hubbard model: exact diagonalization study

A model to describe electronic correlations in energy bands is considered. The model is a generalization of the conventional Hubbard model that allows for the fact that the wavefunction for two electrons occupying the same Wannier orbital is different from the product of single electron wavefunctions. We diagonalize the Hamiltonian exactly on a four-site cluster and study its properties as function of band filling. The quasiparticle weight is found to decrease and the quasiparticle effective mass to increase as the electronic band filling increases, and spectral weight in one- and two-particle spectral functions is transfered from low to high frequencies as the band filling increases. Quasiparticles at the Fermi energy are found to be more 'dressed' when the Fermi level is in the upper half of the band (hole carriers) than when it is in the lower half of the band (electron carriers). The effective interaction between carriers is found to be strongly dependent on band filling becoming less repulsive as the band filling increases, and attractive near the top of the band in certain parameter ranges. The effective interaction is most attractive when the single hole carriers are most heavily dressed, and in the parameter regime where the effective interaction is attractive, hole carriers are found to 'undress', hence become more like electrons, when they pair. It is proposed that these are generic properties of electronic energy bands in solids that reflect a fundamental electron-hole asymmetry of condensed matter. The relation of these results to the understanding of superconductivity in solids is discussed.Comment: Small changes following referee's comment

Theory of nuclear induced spectral diffusion: Spin decoherence of phosphorus donors in Si and GaAs quantum dots

We propose a model for spectral diffusion of localized spins in semiconductors due to the dipolar fluctuations of lattice nuclear spins. Each nuclear spin flip-flop is assumed to be independent, the rate for this process being calculated by a method of moments. Our calculated spin decoherence time $T_{M}=0.64$ ms for donor electron spins in Si:P is a factor of two longer than spin echo decay measurements. For $^{31}$P nuclear spins we show that spectral diffusion is well into the motional narrowing regime. The calculation for GaAs quantum dots gives $T_{M}=10-50$ $\mu$s depending on the quantum dot size. Our theory indicates that nuclear induced spectral diffusion should not be a serious problem in developing spin-based semiconductor quantum computer architectures.Comment: 15 pages, 9 figures. Accepted for publication in Phys. Rev.

Local Dynamics and Strong Correlation Physics I: 1D and 2D Half-filled Hubbard Models

We report on a non-perturbative approach to the 1D and 2D Hubbard models that is capable of recovering both strong and weak-coupling limits. We first show that even when the on-site Coulomb repulsion, U, is much smaller than the bandwith, the Mott-Hubbard gap never closes at half-filling in both 1D and 2D. Consequently, the Hubbard model at half-filling is always in the strong-coupling non-perturbative regime. For both large and small U, we find that the population of nearest-neighbour singlet states approaches a value of order unity as $T\to 0$ as would be expected for antiferromagnetic order. We also find that the double occupancy is a smooth monotonic function of U and approaches the anticipated non-interacting limit and large U limits. Finally, in our results for the heat capacity in 1D differ by no more than 1% from the Bethe ansatz predictions. In addition, we find that in 2D, the heat capacity vs T for different values of U exhibits a universal crossing point at two characteristic temperatures as is seen experimentally in a wide range of strongly-correlated systems such as $^3He$, $UBe_3$, and $CeCu_{6-x}Al_x$. The success of this method in recovering well-established results that stem fundamentally from the Coulomb interaction suggests that local dynamics are at the heart of the physics of strongly correlated systems.Comment: 10 pages, 16 figures included in text, Final version for publication with a reference added and minor corrections. Phys. Rev. B, in pres

Photoemission spectra of Sr2CuO2Cl2{\rm Sr_2 Cu O_2 Cl_2}: a theoretical analysis

Recent angle resolved photoemission (ARPES) results for the insulating cuprate ${\rm Sr_2 Cu O_2 Cl_2}$ have provided the first experimental data which can be directly compared to the (theoretically) well--studied problem of a single hole propagating in an antiferromagnet. The ARPES results reported a small bandwidth, providing evidence for the existence of strong correlations in the cuprates. However, in the same experiment some discrepancies with the familiar 2D ${\rm t-J}$ model were also observed. Here we discuss a comparison between the ARPES results and the quasiparticle dispersion of both (i) the ${\rm t-t'-J}$ Hamiltonian and (ii) the three--band Hubbard model in the strong--coupling limit. Both model Hamiltonians show that the experimentally observed one--hole band structure can be approximately reproduced using reasonable values for ${\rm t'}$, or the direct oxygen hopping amplitude ${\rm t_{pp}}$.Comment: 11 pages, RevTex version 3.0, 3 postscript figures, LaTeX file and figures have been uuencoded

Generalized hole-particle transformations and spin reflection positivity in multi-orbital systems

We propose a scheme combining spin reflection positivity and generalized hole-particle and orbital transformations to characterize the symmetry properties of the ground state for some correlated electron models on bipartite lattices. In particular, we rigorously determine at half-filling and for different regions of the parameter space the spin, orbital and $\eta$ pairing pseudospin of the ground state of generalized two-orbital Hubbard models which include the Hund's rule coupling.Comment: 6 pages, 2 figure