TBA and TCSA with boundaries and excited states |
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| Institution: | 1. Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, England, UK;2. Service de Physique Théorique, CEA-Saclay, F-91191 Gif-sur-Yvette Cedex, France;3. Mathematics Department, King''s College London, Strand, London WC2R 2LS, UK;1. Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany;2. DESY, Theory Group, Notkestraße 85, 22603 Hamburg, Germany;3. Laboratoire de Mathématiques et Physique Théorique CNRS, Université de Tours, Parc de Grammont, 37200 Tours, France;1. Institutt for matematiske fag, NTNU, N-7491 Trondheim, Norway;2. Department of Mathematics, Indiana University, Bloomington, IN 47405, USA;3. Department of Mathematics, Texas A & M University, College Station, TX 77843, USA;1. Departamento de Fisica Fundamental, University of Salamanca, Spain;2. CMCC, Universidade Federal do ABC, Santo Andre, Sao Paulo, Brazil;3. Physics Department, Tomsk State University, Tomsk, Russia |
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| Abstract: | We study the spectrum of the scaling Lee-Yang model on a finite interval from two points of view: via a generalisation of the truncated conformal space approach to systems with boundaries, and via the boundary thermodynamic Bethe ansatz. This allows reflection factors to be matched with specific boundary conditions, and leads us to propose a new (and non-minimal) family of reflection factors to describe the one relevant boundary perturbation in the model. The equations proposed previously for the ground state on an interval must be revised in certain regimes, 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. |
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