Rationality of moduli of vector bundles on curves

The moduli space M(r,d) of stable, rank r, degree d vector bundles on a smooth projective curve of genus g>1 is shown to be birational to M(h,0) x A, where h=hcf(r,d) and A is affine space of dimension (r^2-h^2)(g-1). The birational isomorphism is compatible with fixing determinants in M(r,d) and M(h,0) and we obtain as a corollary that the moduli space of bundles of rank r and fixed determinant of degree d is rational, when r and d are coprime. A key ingredient in the proof is the use of a naturally defined Brauer class for the function field of M(r,d).Comment: 21 pages, Latex2e (with AMS packages

Spectral edge mode in interacting one-dimensional systems

A continuum of excitations in interacting one-dimensional systems is bounded from below by a spectral edge that marks the lowest possible excitation energy for a given momentum. We analyse short-range interactions between Fermi particles and between Bose particles (with and without spin) using Bethe-Ansatz techniques and find that the dispersions of the corresponding spectral edge modes are close to a parabola in all cases. Based on this emergent phenomenon we propose an empirical model of a free, non-relativistic particle with an effective mass identified at low energies as the bare electron mass renormalised by the dimensionless Luttinger parameter $K$ (or $K_\sigma$ for particles with spin). The relevance of the Luttinger parameters beyond the low energy limit provides a more robust method for extracting them experimentally using a much wide range of data from the bottom of the one-dimensional band to the Fermi energy. The empirical model of the spectral edge mode complements the mobile impurity model to give a description of the excitations in proximity of the edge at arbitrary momenta in terms of only the low energy parameters and the bare electron mass. Within such a framework, for example, exponents of the spectral function are expressed explicitly in terms of only a few Luttinger parameters.Comment: 11 pages, 7 figure

Luttinger parameters of interacting fermions in 1D at high energies

Interactions between electrons in one-dimension are fully described at low energies by only a few parameters of the Tomonaga-Luttinger model which is based on linearisation of the spectrum. We consider a model of spinless fermions with a short range interaction via the Bethe-Ansatz technique and show that a Luttinger parameter emerges in an observable beyond the low energy limit. A distinct feature of the spectral function, the edge that marks the lowest possible excitation energy for a given momentum, is parabolic for arbitrary momenta and the prefactor is a function of the Luttinger parameter, K.Comment: 7 pages, 4 figure

Small-angle scattering in a marginal Fermi-liquid

We study the magnetotransport properties of a model of small-angle scattering in a marginal Fermi liquid. Such a model has been proposed by Varma and Abrahams [Phys. Rev. Lett. 86, 4652 (2001)] to account for the anomalous temperature dependence of in-plane magnetotransport properties of the high-Tc cuprates. We study the resistivity, Hall angle and magnetoresistance using both analytical and numerical techniques. We find that small-angle scattering only generates a new temperature dependence for the Hall angle near particle-hole symmetric Fermi surfaces where the conventional Hall term vanishes. The magnetoresistance always shows Kohler's rule behavior.Comment: 4 pages, 3 figures, Revtex

Phase diagram and quasiparticle properties of the Hubbard model within cluster two-site DMFT

We present a cluster dynamical mean-field treatment of the Hubbard model on a square lattice to study the evolution of magnetism and quasiparticle properties as the electron filling and interaction strength are varied. Our approach for solving the dynamical mean-field equations is an extension of Potthoff's "two-site" method [Phys. Rev. B. 64, 165114 (2001)] where the self-consistent bath is represented by a highly restricted set of states. As well as the expected antiferromagnetism close to half filling, we observe distortions of the Fermi surface. The proximity of a van Hove point and the incipient antiferromagnetism lead to the evolution from an electron-like Fermi surface away from the Mott transition, to a hole-like one near half-filling. Our results also show a gap opening anisotropically around the Fermi surface close to the Mott transition (reminiscent of the pseudogap phenomenon seen in the cuprate high-Tc superconductors). This leaves Fermi arcs which are closed into pockets by lines with very small quasiparticle residue.Comment: 10 pages, 8 figures, latex (revtex4

Phenomenological Transport Equation for the Cuprate Metals

We observe that the appearance of two transport relaxation times in the various transport coefficients of cuprate metals may be understood in terms of scattering processes that discriminate between currents that are even, or odd under the charge conjugation operator. We develop a transport equation that illustrates these ideas and discuss its experimental and theoretical consequences.Comment: Replaced with journal ref. Latex+ p