Spectra of Quantum Chains without the Yang-Baxter Equation

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 7 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.

30 pages, LaTeX, preprint Bonn HE-94-09 (small LaTeX problems fixed)

References in corpus (5)

• Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
• On U_q(SU(2))-symmetric Driven Diffusion
• Boundary-Induced Phase Transitions in Equilibrium and Non-Equilibrium Systems
• Reaction-Diffusion Processes as Physical Realizations of Hecke Algebras
• A Two Parameter Deformation of the SU(1/1) Superalgebra and the XY Quantum Chain in a Magnetic Field

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