Year: 2018
Type: article
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.
Institutions: Princeton University, The University of Melbourne, Technische Universität Dresden, Centre National de la Recherche Scientifique, Université Paris Sciences et Lettres, École Normale Supérieure - PSL, Sorbonne Université, Sorbonne Paris Cité, Laboratoire de Physique Théorique et Hautes Energies, Laboratoire de Physique de l'Ecole Normale Supérieure, Université Paris Diderot, Université Pierre-et-Marie-Curie, Donostia International Physics Center
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, U.S. Department of Energy, Deutsche Forschungsgemeinschaft, Materials Research Science and Engineering Center, Harvard University, Multidisciplinary University Research Initiative, Australian Research Council, Office of Naval Research, Division of Materials Research, Army Research Office
Awards: G1207532697, G1268236209, G1338293535, G1349703009, G1375169175, Princeton Center for Complex Materials, G1601203097, G1829435969, G280828947, G3224369381, New physics with strongly correlated and spin-orbit-coupled electrons, G4353487559, EAGER: Topological Semimetals, Insulators and Supersymmetry, G6918153286, NEW TOPOLOGICAL FRONTIER, G732077798, G7452299184, G8876996369, G936330020
OpenAlex ID: W2749443713