Scaling Relation for Excitation Energy Under Hyperbolic Deformation

We introduce a one-parameter deformation for one-dimensional (1D) quantum lattice models, the hyperbolic deformation, where the scale of the local energy is proportional to cosh lambda j at the j-th site. Corresponding to a 2D classical system, the deformation does not strongly modify the ground state. In this situation, the effective Hamiltonian of the quantum system shows that the quasi particle is weakly bounded around the center of the system. By analyzing this binding effect, we derive scaling relations for the mean-square width of confinement, the energy correction with respect to the excitation gap \Delta, and the deformation parameter $\lambda$. This finite-size scaling allows us to investigate excitation gap of 1D non-deformed bulk quantum systems.Comment: 9 pages, 5 figure

Theorems on ground-state phase transitions in Kohn-Sham models given by the Coulomb density functional

Some theorems on derivatives of the Coulomb density functional with respect to the coupling constant $\lambda$ are given. Consider an electron density $n_{GS}({\bf r})$ given by a ground state. A model Fermion system with the reduced coupling constant, $\lambda<1$, is defined to reproduce $n_{GS}({\bf r})$ and the ground state energy. Fixing the charge density, possible phase transitions as level crossings detected in a value of the reduced density functional happen only at discrete points along the $\lambda$ axis. If the density is $v$-representable also for $\lambda<1$, accumulation of phase transition points is forbidden when $\lambda\rightarrow 1$. Relevance of the theorems for the multi-reference density functional theory is discussed.Comment: 19 page

Redox functionality mediated by adsorbed oxygen on a Pd-oxide film over a Pd(100) thin structure: A first-principles study

Stable oxygen sites on a PdO film over a Pd(100) thin structures with a (sqrt{5} times sqrt{5}) R27^circ surface-unit cell are determined using the first-principles electronic structure calculations with the generalized gradient approximation. The adsorbed monatomic oxygen goes to a site bridging two 2-fold-coordinated Pd atoms or to a site bridging a 2-fold-coordinated Pd atom and a 4-fold-coordinated Pd atom. Estimated reaction energies of CO oxidation by reduction of the oxidized PdO film and N_2O reduction mediated by oxidation of the PdO film are exothermic. Motion of the adsorbed oxygen atom between the two stable sites is evaluated using the nudged elastic band method, where an energy barrier for a translational motion of the adsorbed oxygen may become sim 0.45 eV, which is low enough to allow fluxionality of the surface oxygen at high temperatures. The oxygen fluxionality is allowed by existence of 2-fold-coordinated Pd atoms on the PdO film, whose local structure has similarity to that of Pd catalysts for the Suzuki-Miyaura cross coupling. Although NO_x (including NO_2 and NO) reduction is not always catalyzed only by the PdO film, we conclude that there may happen continual redox reactions mediated by oxygen-adsorbed PdO films over a Pd surface structure, when the influx of NO_x and CO continues, and when the reaction cycle is kept on a well-designed oxygen surface.Comment: 15 pages, 6 figures, submitted to J. Phys. Condens. Matte

Spin-twist driven persistent current in a strongly correlated two-dimensional electron system: a manifestation of the gauge field

A persistent current, coupled with the spin state, of purely many-body origin is shown to exist in Nagaoka's ferromagnetic state in two dimensions (2D). This we regard as a manifestation of a gauge field, which comes from the surrounding spin configuration and acts on the hole motion, being coupled to the Aharonov-Bohm flux. This provides an example where the electron-electron interaction exerts a profound effect involving the spins in clean two-dimensional lattice systems in sharp contrast to continuum or spinless fermion systems.Comment: 11 pages, typeset using Revtex 3.0, Phys. Rev. B in press, 2 figures available upon request at [email protected]

Spectral function of the spiral spin state in the trestle and ladder Hubbard model

Eder and Ohta have found a violation of the Luttinger rule in the spectral function for the t-t'-J model, which was interpreted as a possible breakdown of the Tomonaga-Luttinger(TL) description in models where electrons can pass each other. Here we have computed the spin correlation along with the spectral function for the one-dimensional t-t' Hubbard model and two-leg Hubbard ladder. By varying the Hubbard U we have identified that such a phenomenon is in fact a spinless-fermion-like behavior of holes moving in a spiral spin configuration that has a spin correlation length of the system size.Comment: 3 pages, RevTex, 8 figures in Postscript, to be published in Phys. Rev. B (rapid communication

Thermodynamics and excitations of the one-dimensional Hubbard model

We review fundamental issues arising in the exact solution of the one-dimensional Hubbard model. We perform a careful analysis of the Lieb-Wu equations, paying particular attention to so-called `string solutions'. Two kinds of string solutions occur: $\Lambda$ strings, related to spin degrees of freedom and $k-\Lambda$ strings, describing spinless bound states of electrons. Whereas $\Lambda$ strings were thoroughly studied in the literature, less is known about $k-\Lambda$ strings. We carry out a thorough analytical and numerical analysis of $k-\Lambda$ strings. We further review two different approaches to the thermodynamics of the Hubbard model, the Yang-Yang approach and the quantum transfer matrix approach, respectively. The Yang-Yang approach is based on strings, the quantum transfer matrix approach is not. We compare the results of both methods and show that they agree. Finally, we obtain the dispersion curves of all elementary excitations at zero magnetic field for the less than half-filled band by considering the zero temperature limit of the Yang-Yang approach.Comment: 72 pages, 11 figures, revte

Ferromagnetism in a Hubbard model for an atomic quantum wire: a realization of flat-band magnetism from even-membered rings

We have examined a Hubbard model on a chain of squares, which was proposed by Yajima et al as a model of an atomic quantum wire As/Si(100), to show that the flat-band ferromagnetism according to a kind of Mielke-Tasaki mechanism should be realized for an appropriate band filling in such a non-frustrated lattice. Reflecting the fact that the flat band is not a bottom one, the ferromagnetism vanishes, rather than intensified, as the Hubbard U is increased. The exact diagonalization method is used to show that the critical value of U is in a realistic range. We also discussed the robustness of the magnetism against the degradation of the flatness of the band.Comment: misleading terms and expressions are corrected, 4 pages, RevTex, 5 figures in Postscript, to be published in Phys. Rev. B (rapid communication

Flat-band ferromagnetism induced by off-site repulsions

Density matrix renormalization group method is used to analyze how the nearest-neighbor repulsion V added to the Hubbard model on 1D triangular lattice and a railway trestle (t-t') model will affect the electron-correlation dominated ferromagnetism arising from the interference (frustration). Obtained phase diagram shows that there is a region in smaller-t' side where the critical on-site repulsion above which the system becomes ferromagnetic is reduced when the off-site repulsion is introduced.Comment: 4 pages, RevTex, 6 figures in Postscript, to be published in Phys. Rev.