Spectra of Quantum Chains without the Yang-Baxter Equation

TL;DR

This paper analyzes non-integrable quantum chains derived from reaction-diffusion models, providing exact energy spectra and applying the results to determine the dynamical critical exponent of a novel kinetic Ising model.

Contribution

It introduces a method to solve certain reaction-diffusion models without relying on the Yang-Baxter equation, revealing new energy spectra for complex quantum chains.

Findings

Derived $L (L - 1) + 1$ energy levels for a quantum chain with $L$ sites.

Identified a new class of non-integrable Hamiltonians depending on 7 parameters.

Computed the dynamical critical exponent for a novel kinetic Ising model.

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.