Exact Excited States of Non-Integrable Models

TL;DR

This paper introduces a numerical method to identify and derive exact excited states in non-integrable models, exemplified by the AKLT model, revealing a tower of states and insights into the Eigenstate Thermalization Hypothesis.

Contribution

The authors develop a novel numerical approach to find exact excited states in non-integrable models and derive analytic expressions for a tower of such states in the AKLT model.

Findings

Exact analytic expressions for a tower of excited states in the AKLT model

Identification of states spanning from ground to highest excited energy levels

Conjectures on the Eigenstate Thermalization Hypothesis based on bulk states

Abstract

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. To our knowledge, this is the first time that exact analytic expressions for a tower of excited states have been found in non-integrable models. Some of the states of the tower appear to be in the bulk of the energy spectrum, allowing us to make conjectures on the strong Eigenstate Thermalization Hypothesis (ETH). We also generalize these exact states including the tower of states to the generalized integer spin AKLT models. Furthermore, we establish a correspondence between some of our states and those of the Majumdar-Ghosh model, yet another non-integrable model, and extend our construction to the generalized integer spin AKLT models.