The renormalization of the effective Lagrangian with spontaneous symmetry breaking: the SU(2) case

We study the renormalization of the nonlinear effective SU(2) Lagrangian up to $O(p^4)$ with spontaneous symmetry breaking. The Stueckelberg transformation, the background field gauge, the Schwinger proper time and heat kernel method, and the covariant short distance expansion technology, guarantee the gauge covariance and incooperate the Ward indentities in our calculations. The renormalization group equations of the effective couplings are derived and analyzed. We find that the difference between the results gotten from the direct method and the renormalization group equation method can be quite large when the Higgs scalar is far below its decoupling limit.Comment: ReVTeX, 12 figures, 22 pages, some bugs are kicked off from programs, numerical analysis is renew

Coordinate Representation of the One-Spinon One-Holon Wavefunction and Spinon-Holon Interaction

By deriving and studying the coordinate representation for the one-spinon one-holon wavefunction we show that spinons and holons in the supersymmetric $t - J$ model with $1/r^2$ interaction attract each other. The interaction causes a probability enhancement in the one-spinon one-holon wavefunction at short separation between the particles. We express the hole spectral function for a finite lattice in terms of the probability enhancement, given by the one-spinon one-holon wavefunction at zero separation. In the thermodynamic limit, the spinon-holon attraction turns into the square-root divergence in the hole spectral function.Comment: 20 pages, 3 .eps figure

Application of the Density Matrix Renormalization Group in momentum space

We investigate the application of the Density Matrix Renormalization Group (DMRG) to the Hubbard model in momentum-space. We treat the one-dimensional models with dispersion relations corresponding to nearest-neighbor hopping and $1/r$ hopping and the two-dimensional model with isotropic nearest-neighbor hopping. By comparing with the exact solutions for both one-dimensional models and with exact diagonalization in two dimensions, we first investigate the convergence of the ground-state energy. We find variational convergence of the energy with the number of states kept for all models and parameter sets. In contrast to the real-space algorithm, the accuracy becomes rapidly worse with increasing interaction and is not significantly better at half filling. We compare the results for different dispersion relations at fixed interaction strength over bandwidth and find that extending the range of the hopping in one dimension has little effect, but that changing the dimensionality from one to two leads to lower accuracy at weak to moderate interaction strength. In the one-dimensional models at half-filling, we also investigate the behavior of the single-particle gap, the dispersion of spinon excitations, and the momentum distribution function. For the single-particle gap, we find that proper extrapolation in the number of states kept is important. For the spinon dispersion, we find that good agreement with the exact forms can be achieved at weak coupling if the large momentum-dependent finite-size effects are taken into account for nearest-neighbor hopping. For the momentum distribution, we compare with various weak-coupling and strong-coupling approximations and discuss the importance of finite-size effects as well as the accuracy of the DMRG.Comment: 15 pages, 11 eps figures, revtex

Nonresonant inelastic light scattering in the Hubbard model

Inelastic light scattering from electrons is a symmetry-selective probe of the charge dynamics within correlated materials. Many measurements have been made on correlated insulators, and recent exact solutions in large dimensions explain a number of anomalous features found in experiments. Here we focus on the correlated metal, as described by the Hubbard model away from half filling. We can determine the B1g Raman response and the inelastic X-ray scattering along the Brillouin zone diagonal exactly in the large dimensional limit. We find a number of interesting features in the light scattering response which should be able to be seen in correlated metals such as the heavy fermions.Comment: 9 pages, 7 figures, typeset with ReVTe

Split-off dimer defects on the Si(001)2x1 surface

Dimer vacancy (DV) defect complexes in the Si(001)2x1 surface were investigated using high-resolution scanning tunneling microscopy and first principles calculations. We find that under low bias filled-state tunneling conditions, isolated 'split-off' dimers in these defect complexes are imaged as pairs of protrusions while the surrounding Si surface dimers appear as the usual 'bean-shaped' protrusions. We attribute this to the formation of pi-bonds between the two atoms of the split-off dimer and second layer atoms, and present charge density plots to support this assignment. We observe a local brightness enhancement due to strain for different DV complexes and provide the first experimental confirmation of an earlier prediction that the 1+2-DV induces less surface strain than other DV complexes. Finally, we present a previously unreported triangular shaped split-off dimer defect complex that exists at SB-type step edges, and propose a structure for this defect involving a bound Si monomer.Comment: 8 pages, 7 figures, submitted to Phys. Rev.

Site 1217

Site 1217 (16°52.02´N, 138°06.00´W; 5342 meters below sea level [mbsl]; Fig. F1) is one of seven sites drilled to target upper Paleocene crust along a latitudinal transect during Leg 199 and will be used to investigate paleoceanographic processes in the northern tropical early Eocene Pacific Ocean. Site 1217 is situated ~1° north of the Clarion Fracture Zone on abyssal hill topography typical of the central Pacific. Based on magnetic lineations, basement age at Site 1217 should be in magnetic Anomaly C25r or ~57 Ma (Cande et al., 1989; timescale of Cande and Kent, 1995). The Cenozoic history of sedimentation in this region was poorly constrained prior to Leg 199 drilling because the nearest drill site (Deep Sea Drilling Project [DSDP] Site 162) is situated ~300 km south and west on 48-Ma crust. Based on data from this early rotary-cored hole, magnetic anomaly maps, a shallow-penetration piston core near Site 1217 (EW9709-4PC), and seismic profiling (Fig. F2), we expected the sedimentary sequence at Site 1217 to comprise a relatively thick (25 to 35 m thick) section of red clays overlying a radiolarian ooze and a basal carbonate section with possible chert near basement (estimated total depth ~125-150 meters below seafloor [mbsf]) deposited when the site was near the ridge crest in the late Paleocene and early Eocene. Site 1217 was chosen because it is anticipated to have been located just outside of the equatorial region at 56 Ma, ~5°N, 106°W based upon a fixed hotspot model (Gripp and Gordon, 1990, for 0- to 5-Ma Pacific hotspot rotation pole; Engebretson et al., 1985, for older poles). On the same basis at 40 Ma, the site was located at ~8°N, 111°W. Thus, Site 1217 should help define the paleoceanography of the northern tropical Pacific, in particular locating the ancient North Equatorial Countercurrent (NECC) region. General circulation-model experiments for the early Eocene (see Huber, this volume) suggest that the NECC was a well-developed current during this time period. Other paleoceanographic and paleoclimatic objectives of drilling the sedimentary sequence anticipated at Site 1217 are as follows: (1) to help define the shift in the Intertropical Convergence Zone through the Paleogene by following the change in eolian dust composition and flux through time (red clays); (2) to help constrain the middle-late Eocene calcite compensation depth (CCD); and (3) to sample the Paleocene/Eocene (P/E) boundary, one of the most climatologically critical intervals of Cenozoic time. Recovery of deep-sea sediments from this time interval during Leg 199 is a high priority because the P/E boundary has never before been sampled in the central tropical Pacific Ocean. Results from Site 1217 will also provide important information to test whether there was significant motion of the Hawaiian hotspot, with respect to the Earth's spin axis during the early Cenozoic. At 56 Ma, the backtracked location based upon a hotspot reference frame is ~5°N, 106°W, and at 40 Ma is ~8°N, 106°W. If significant hotspot motion or true polar wander occurred since 57 Ma (Petronotis et al., 1994), this drill site could have been much nearer to the equator

Site 1220

Site 1220 (10°10.600´N, 142°45.503´W; 5218 meters below sea level (mbsl); Fig. F1) forms a southerly component of the 56-Ma transect drilled during Leg 199. It is situated about midway between the Clipperton and Clarion Fracture Zones in typical abyssal hill topography. On the basis of regional magnetic anomalies, we anticipated basement age at Site 1220 to be equivalent to Chron C25n (~56 Ma; Cande et al., 1989), slightly older than at Site 1219. At the outset of drilling at Site 1220, our estimate for total sediment depth was ~225 meters below seafloor (mbsf) (Fig. F2). Based upon a fixed hotspot model (Gripp and Gordon, 1990, for 0- to 5-Ma Pacific hotspot rotation pole; Engebretson et al., 1985, for older poles), Site 1220 should have been located ~3° south of the equator at 56 Ma and in an equatorial position at 40 Ma. Thus, Site 1220 should have been situated underneath the South Equatorial Current in the early Eocene. A nearby piston core (EW9709-13PC) taken during the site survey cruise recovered >16 m of red clay, with the base of the core dated as middle-early Miocene on the basis of radiolarian biostratigraphy (Lyle, 2000). Site 1220 will be used to study equatorial ocean circulation from the late Paleocene through the late Eocene during the early Cenozoic thermal maximum. Sediment records from this site will help to define the calcite compensation depth (CCD) and lysocline during the Paleocene-Eocene and Eocene-Oligocene transitions. In this and other respects, Site 1220 will act as an interesting analog to Site 1218. Both sites are thought to have been located on the equator at ~40 Ma, but the older crustal age anticipated at Site 1220 dictates a greater paleowater depth than for contemporaneous sediments accumulating at Site 1218