RVB gauge theory and the Topological degeneracy in the Honeycomb Kitaev model

We relate the Z$_2$ gauge theory formalism of the Kitaev model to the SU(2) gauge theory of the resonating valence bond (RVB) physics. Further, we reformulate a known Jordan-Wigner transformation of Kitaev model on a torus in a general way that shows that it can be thought of as a Z$_2$ gauge fixing procedure. The conserved quantities simplify in terms of the gauge invariant Jordan-Wigner fermions, enabling us to construct exact eigen states and calculate physical quantities. We calculate the fermionic spectrum for flux free sector for different gauge field configurations and show that the ground state is four-fold degenerate on a torus in thermodynamic limit. Further on a torus we construct four mutually anti-commuting operators which enable us to prove that all eigenstates of this model are four fold degenerate in thermodynamic limit.Comment: 12 pages, 3 figures. Added affiliation and a new section, 'Acknowledgements'.Typos correcte

Response of a spaceborne gravitational wave antenna to solar oscillations

We investigate the possibility of observing very small amplitude low frequency solar oscillations with the proposed laser interferometer space antenna (LISA). For frequencies $\nu$ below $3\times 10^{-4} {\rm Hz}$ the dominant contribution is from the near zone time dependent gravitational quadrupole moments associated with the normal modes of oscillation. For frequencies $\nu$ above $3\times 10^{-4} {\rm Hz}$ the dominant contribution is from gravitational radiation generated by the quadrupole oscillations which is larger than the Newtonian signal by a factor of the order $(2 \pi r \nu/ c)^4$, where $r$ is the distance to the Sun, and $c$ is the velocity of light. The low order solar quadrupole pressure and gravity oscillation modes have not yet been detected above the solar background by helioseismic velocity and intensity measurements. We show that for frequencies $\nu \lesssim 2\times 10^{-4} {\rm Hz}$, the signal due to solar oscillations will have a higher signal to noise ratio in a LISA type space interferometer than in helioseismology measurements. Our estimates of the amplitudes needed to give a detectable signal on a LISA type space laser interferometer imply surface velocity amplitudes on the sun of the order of 1-10 mm/sec in the frequency range $1\times 10^{-4} -5\times 10^{-4} {\rm Hz}$. If such modes exist with frequencies and amplitudes in this range they could be detected with a LISA type laser interferometer.Comment: 16 pages, 6 figures, 1 table. A reworked and considerably improved version of ArXiv:astro-ph/0103472, Published in PR

Superconducting Gap Nodal Surface and Fermi Surface: their partial overlap in cuprates

Electron correlation in cuprates leads to a global constraint $\sum_{\bf k} \Delta_{\bf k} = 0$ on the gap function $\Delta_{\bf k}$ resulting in a gap nodal surface. We give physical arguments supported by numerical results and discuss some experimental results to argue that correlations also lead to a local constraint on charge fluctuations in ${\bf k}$-space close to the Fermi surface, which may result in a substantial overlap of the Fermi surface with the gap nodal surface.Comment: RevTeX 3.0, 4 Pages, 6 PostScript Figures

g-on Mean Field Theory of the t-J Model

Implication of our recent proposal [J. Phys. Soc. Jpn. 65 (1996) 687] to treat large-amplitude gauge-field fluctuations around the slave-boson mean-field theory for the t-J model has been explored in detail. By attaching gauge flux to spinons and holons and then treating them as free g-on's which respect the time-reversal symmetry, the optimum exclusion (g) and exchange (\a) statistics have been determined in the plane of doping rate and temperature. Two different relations between \a and g have been investigated, namely g=|\a| (Case1) and g=|\a|(2-|\a|) (Case2). The results indicate that slave fermion is favored at low doping while slave boson at high doping. For two dimension, in Case1 intermediate statistics are found in between, while in Case2 no intermediate statistics are found. The consequences of varying the dimensionality and strength of J have been studied also. The latter has no qualitative effect for both cases, while the former has a profound effect in Case1.Comment: 18 pages, 11 figures two of them are figure 8; submitted to Phys. Rev. B; notes and citations are added, as seen in page 17; E-mails: [email protected], [email protected]

Quantum ether: photons and electrons from a rotor model

We give an example of a purely bosonic model -- a rotor model on the 3D cubic lattice -- whose low energy excitations behave like massless U(1) gauge bosons and massless Dirac fermions. This model can be viewed as a ``quantum ether'': a medium that gives rise to both photons and electrons. It illustrates a general mechanism for the emergence of gauge bosons and fermions known as ``string-net condensation.'' Other, more complex, string-net condensed models can have excitations that behave like gluons, quarks and other particles in the standard model. This suggests that photons, electrons and other elementary particles may have a unified origin: string-net condensation in our vacuum.Comment: 10 pages, 6 figures, RevTeX4. Home page http://dao.mit.edu/~we