Exact Excited States of Non-Integrable Models

Understand

We discuss a method of numerically identifying exact energy eigenstates for a finite system, whose form can then be obtained analytically.

• We demonstrate our method by identifying and deriving exact analytic expressions for several excited states, including an infinite tower, of the one dimensional spin-1 AKLT model, a celebrated non-integrable model.
• The states thus obtained for the AKLT model can be interpreted as one-to-an extensive number of quasiparticles on the ground state or on the highest excited state when written in terms of dimers.
• Included in these exact states is a tower of states spanning energies from the ground state to the highest excited state.