arXiv subjects
Publications and source records attributed to Roberto Tateo.
The method of analytic continuation is used to find exact integral equations for a selection of finite-volume energy levels for the non-unitary minimal models $M_{2,2N+3}$ perturbed by their $φ_{13}$ operators. The N=2 case is studied in particular detail. Along the way, we find a number of general results which should be relevant to the study of excited states in other models.
The generally accepted phase diagrams for the discrete $Z_N$ spin models in two dimensions imply the existence of certain renormalisation group flows, both between conformal field theories and into a massive phase. Integral equations are proposed to describe these flows, and some properties of their solutions are discussed. The infrared behaviour in massless and massive directions is analysed in detail, and the techniques used are applied to a number of other models.
We suggest an approach to the problem of finding integral equations for the excited states of an integrable model, starting from the Thermodynamic Bethe Ansatz equations for its ground state. The idea relies on analytic continuation through complex values of the coupling constant, and an analysis of the monodromies that the equations and their solutions undergo. For the scaling Lee-Yang model, we find equations in this way for the one- and two- particle states in the spin-zero sector, and suggest various generalisations. Numerical results show excellent agreement with the truncated conformal space approach, and we also treat some of the ultraviolet and infrared asymptotics analytically.