Gauge-theory approach to planar doped antiferromagnets and external magnetic fields

A review is given of a relativistic non-Abelian gauge theory approach to the physics of spin-charge separation in doped quantum antiferromagnetic planar systems, proposed recently by the authors. Emphasis is put on the effects of constant external magnetic fields on excitations about the superconducting state in the model. The electrically-charged Dirac fermions (holons), describing excitations about specific points on the fermi surface, e.g. those corresponding to the nodes of a d-wave superconducting gap in high-$T_c$ cuprates, condense, resulting in the opening of a Kosterlitz-Thouless-like gap (KT) at such nodes. In the presence of strong external magnetic fields at the surface regions of the planar superconductor, in the direction perpendicular to the superconducting planes, these KT gaps appear to be enhanced. Our preliminary analysis, based on analytic Scwhinger-Dyson treatments, seems to indicate that for an even number of Dirac fermion species, required in our model as a result of gauging a particle-hole SU(2) symmetry, Parity or Time Reversal violation does not necessarily occurs.Based on these considerations, we argue that recent experimental findings, concerning thermal conductivity plateaux of quasiparticles in planar high-$T_c$ cuprates in strong external magnetic fields, may indicate the presence of such KT gaps, caused by charged Dirac-fermion excitations in these materials, as suggested in the above model.Comment: 26 pages LATEX, 6 figures (incorporated) (In this revised version references on magnetic catalysis were added, and also a note was added with a comparison of the theoretical results presented here with a second experiment (cond-mat/9709061), reporting on unconventional superconducting phases in certain cuprates). Journal ref.:Based on Invited talk by N.E.M. at the `5th Chia Workshop on Common Trends in Particle and Condensed Matter Physics', Conference Center, Grand-Hotel Chia-Laguna, Chia, Italy, 1-11 September 199

Ab initio Translationally Invariant Nonlocal One-body Densities from No-core Shell-model Theory

[Background:] It is well known that effective nuclear interactions are in general nonlocal. Thus if nuclear densities obtained from {\it ab initio} no-core-shell-model (NCSM) calculations are to be used in reaction calculations, translationally invariant nonlocal densities must be available. [Purpose:] Though it is standard to extract translationally invariant one-body local densities from NCSM calculations to calculate local nuclear observables like radii and transition amplitudes, the corresponding nonlocal one-body densities have not been considered so far. A major reason for this is that the procedure for removing the center-of-mass component from NCSM wavefunctions up to now has only been developed for local densities. [Results:] A formulation for removing center-of-mass contributions from nonlocal one-body densities obtained from NCSM and symmetry-adapted NCSM (SA-NCSM) calculations is derived, and applied to the ground state densities of $^4$He, $^6$Li, $^{12}$C, and $^{16}$O. The nonlocality is studied as a function of angular momentum components in momentum as well as coordinate space [Conclusions:] We find that the nonlocality for the ground state densities of the nuclei under consideration increases as a function of the angular momentum. The relative magnitude of those contributions decreases with increasing angular momentum. In general, the nonlocal structure of the one-body density matrices we studied is given by the shell structure of the nucleus, and can not be described with simple functional forms.Comment: 13 pages, 11 Figure

K_{l3} transition form factors

The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the meson bound state amplitudes and the dressed quark-W vertex in a manifestly covariant calculation of the K_{l3} transition form factors and decay width in impulse approximation. With model gluon parameters previously fixed by the chiral condensate, the pion mass and decay constant, and the kaon mass, our results for the K_{l3} form factors and the kaon semileptonic decay width are in good agreement with the experimental data.Comment: 8 pages, 3 figures, Revte

The π\pi, K+K^+, and K0K^0 electromagnetic form factors

The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the meson amplitudes and the dressed quark-photon vertex in a self-consistent Poincar\'e-invariant study of the pion and kaon electromagnetic form factors in impulse approximation. We demonstrate explicitly that the current is conserved in this approach and that the obtained results are independent of the momentum partitioning in the Bethe-Salpeter amplitudes. With model gluon parameters previously fixed by the condensate, the pion mass and decay constant, and the kaon mass, the charge radii and spacelike form factors are found to be in good agreement with the experimental data.Comment: 8 pages, 6 figures, Revte

Dynamical Gauge Symmetry Breaking and Superconductivity in three-dimensional systems

We discuss dynamical breaking of non-abelian gauge groups in three dimensional (lattice) gauge systems via the formation of fermion condensates. A physically relevant example, motivated by condensed-matter physics, is that of a fermionic gauge theory with group $SU(2)\otimes U_S(1) \otimes U_{E}(1)$. In the strong U_S(1) region, the SU(2) symmetry breaks down to a U(1), due to the formation of a parity-invariant fermion condensate. We conjecture a phase diagram for the theory involving a critical line, which separates the regions of broken SU(2) symmetry from those where the symmetry is restored. In the broken phase, the effective Abelian gauge theory is closely related to an earlier model of two-dimensional parity-invariant superconductivity in doped antiferromagnets. The superconductivity in the model occurs in the Kosterlitz-Thouless mode, since strong phase fluctuations prevent the existence of a local order parameter. Some physical consequences of the $SU(2) \times U_S(1)$ phase diagram for the (doping-dependent) parameter space of this condensed-matter model are briefly discussed.Comment: 17 pages Latex, 1 macro, three figures (included) (minor typo on page 14 concerning the critical coupling of SU(2) corrected

Ab initio Folding Potentials for Nucleon-Nucleus Scattering based on NCSM One-Body Densities

Calculating microscopic optical potentials for elastic nucleon-nucleus scattering has already led to large body of work in the past. For folding first-order calculations the nucleon-nucleon (NN) interaction and the one-body density of the nucleus were taken as input to rigorous calculations in a spectator expansion of the multiple scattering series. Based on the Watson expansion of the multiple scattering series we employ a nonlocal translationally invariant nuclear density derived from a chiral next-to-next-to-leading order (NNLO) and the very same interaction for consistent full-folding calculation of the effective (optical) potential for nucleon-nucleus scattering for light nuclei. We calculate scattering observables, such as total, reaction, and differential cross sections as well as the analyzing power and the spin-rotation parameter, for elastic scattering of protons and neutrons from $^4$He, $^{6}$He, $^{12}$C, and $^{16}$O, in the energy regime between 100 and 200~MeV projectile kinetic energy, and compare to available data. Our calculations show that the effective nucleon-nucleus potential obtained from the first-order term in the spectator expansion of the multiple scattering expansion describes experiments very well to about 60 degrees in the center-of-mass frame, which coincides roughly with the validity of the NNLO chiral interaction used to calculate both the NN amplitudes and the one-body nuclear density.Comment: 10 pages, 14 figures, 1 tabl

Electron-scattering form factors for 6Li in the ab initio symmetry-guided framework

We present an ab initio symmetry-adapted no-core shell-model description for $^{6}$Li. We study the structure of the ground state of $^{6}$Li and the impact of the symmetry-guided space selection on the charge density components for this state in momentum space, including the effect of higher shells. We accomplish this by investigating the electron scattering charge form factor for momentum transfers up to $q \sim 4$ fm$^{-1}$. We demonstrate that this symmetry-adapted framework can achieve significantly reduced dimensions for equivalent large shell-model spaces while retaining the accuracy of the form factor for any momentum transfer. These new results confirm the previous outcomes for selected spectroscopy observables in light nuclei, such as binding energies, excitation energies, electromagnetic moments, E2 and M1 reduced transition probabilities, as well as point-nucleon matter rms radii.Comment: 10 pages, 7 figures; accepted to Physical Review