Exact excited states of nonintegrable models

Sanjay Moudgalya, Stephan Rachel, B. Andrei Bernevig, Nicolas Regnault

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45 Scopus citations

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 Affleck-Kennedy-Lieb-Tasaki (AKLT) model, a celebrated nonintegrable model. The states thus obtained for the AKLT model can be interpreted as from 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. 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. 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 nonintegrable model, and extend our construction to the generalized integer spin AKLT models.

Original languageEnglish (US)
Article number235155
JournalPhysical Review B
Volume98
Issue number23
DOIs
StatePublished - Dec 27 2018

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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