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Spectra of Quantum Chains without the Yang-Baxter Equation

I. Peschel·V. Rittenberg·U. Schultze
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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.

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I. Peschel, V. Rittenberg, U. Schultze. 1994-06-13. Spectra of Quantum Chains without the Yang-Baxter Equation. https://doi.org/10.1016/0550-3213(94)90163-5

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