Exact excited states of nonintegrable models

By Sanjay Moudgalya, S. Rachel, Bogdan Andrei Bernevig, N. Regnault. Physical review B, 2017

233 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/afb91812ab7bff79d81dadda55b12b92cddbda64

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Localization from Hilbert space shattering: From theory to physical realizations (2020, background): “[13] Sanjay Moudgalya, Stephan Rachel, B.”
Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians (2019, background): “This weak fragmentation is reminiscent to what has been observed in other models in the context of many-body quantum scars: although the majority of the eigenstates obey ETH, nonthermal eigenstates exist even in the bulk of the spectrum [33–35, 41, 42].”
Statistical localization: From strong fragmentation to strong edge modes (2019, background): “Several works investigated the possibility of mimicking similarly localized behavior without explicitly breaking translation invariance [25–33], as well as the possibility of intermediate behavior, such as the existence of a small number of ETH-violating eigenstates within an otherwise generic spect”
Quantum Many-Body Scars: A Quasiparticle Perspective (2022, background): “While a variety of mechanisms for quantum many-body scars have been proposed, a ubiquitous one is the emergence of a small subset of stable quasiparticles, out of which special many-particle states throughout the many-body spectrum can be constructed (15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, ”