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Spectra of quantum chains without the Yang-Baxter equation |
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| Authors: | I Peschel V Rittenberg U Schultze |
| Institution: | a Max-Planck-Institut für Physik komplexer Systeme, Bayreuther Strasse 40, Haus 16, 01187, Dresden, Germany b Freie Universität Berlin, Fachbereich Physik, Arnimallee 14, 14195, Berlin, Germany c Physikalisches Institut, Universität Bonn, Nussallee 12, 53115, Bonn, Germany d Laboratoire de Physique Théorique des Liquides, Université Pierre et Marie Curie, 4 Place Jussieu, 75252, Paris Cedex 05, France |
| Abstract: | We study one-dimensional reaction-diffusion models described by master equations and their associated two-state quantum hamiltonians. By choosing appropriate rates, the equations of motion decouple into certain subsets. We solve the first subset which has a close relation to the problem of lattice electrons in an electric field. In this way we obtain L(L − 1) + 1 energy levels of a quantum chain with L sites. The corresponding hamiltonian depends on seven parameters and does not look integrable using conventional methods. As an application, we compute the dynamical critical exponent of a new type of kinetic Ising model. |
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