Maths HEP Lunchtime Seminars: Rigorous construction of generalized Luttinger liquids
20 May 2005 00:00 in CM221
"By exact RG analisys it is possible to compute in a rigorous and explicit way (for small coupling) the correlations of several models like d=1 spin chain models (XYZ, XXZ and perturbations), Vertex or Ashkin Teller models, 1d Hubbard models and so on. No integrability properties are used and no conformal or local gauge symmetry is required. The correlation are written as series which are indeed convergent; convergence follows from determinant bounds for fermions and on a set of approximate Ward identities, where approximate refers to the fact that the presence of masses and ultraviolet cutoffs (like lattice or nonlinear bands) make the WI different from the formal ones for the presence of terms not neglible at all. Ather WIs (never found before) can be used for such extra terms appearing in the WI and by that dramatic cancellations at all order can be proved in the expansions, implying convergence of the series for correlations."