η -pairing in Hubbard models: From spectrum generating algebras to quantum many-body scars
Abstract
We revisit the η -pairing states in Hubbard models and explore their connections to quantum many-body scars to discover a universal scars mechanism. η -pairing occurs due to an algebraic structure known as a spectrum generating algebra (SGA), giving rise to equally spaced towers of eigenstates in the spectrum. We generalize the original η -pairing construction and show that several Hubbard-like models on arbitrary graphs exhibit SGAs, including ones with disorder and spin-orbit coupling. We further define a restricted spectrum generating algebra (RSGA) and give examples of perturbations to the Hubbard-like models that preserve an equally spaced tower of the original model as eigenstates. The states of the surviving tower exhibit a subthermal entanglement entropy, and we analytically obtain parameter regimes for which they lie in the bulk of the spectrum, showing that they are exact quantum many-body scars. The RSGA framework also explains the equally spaced towers of eigenstates in several well-known models of quantum scars, including the Affleck-Kennedy-Lieb-Tasaki model.
- Publication:
-
Physical Review B
- Pub Date:
- August 2020
- DOI:
- 10.1103/PhysRevB.102.085140
- arXiv:
- arXiv:2004.13727
- Bibcode:
- 2020PhRvB.102h5140M
- Keywords:
-
- Condensed Matter - Strongly Correlated Electrons;
- Condensed Matter - Statistical Mechanics;
- Quantum Physics
- E-Print:
- 13 pages v2: typos corrected, references added