TBA AND TCSA WITH BOUNDARIES AND EXCITED-STATES

We study the spectrum of the scaling Lee-Yang model on a finite interv al from two points of view: via a generalisation of the truncated conf ormal space approach to systems with boundaries, and via the boundary thermodynamic Bethe ansatz. This allows reflection factors to be match ed with specific boundary conditions, and leads us to propose a new (a nd non-minimal) family of reflection factors to describe the one relev ant boundary perturbation in the model. The equations proposed previou sly for the ground state on an interval must be revised in certain reg imes, and we find the necessary modifications by analytic continuation . We also propose new equations to describe excited states, and check all equations against boundary truncated conformal space data, Access to the finite-size spectrum enables us to observe boundary flows when the bulk remains massless, and the formation of boundary bound states when the bulk is massive. (C) 1998 Elsevier Science B.V.