Group theoretic approach to many-body scar states in fermionic lattice models

It has been shown [K. Pakrouski et al., Phys. Rev. Lett. 125, 230602 (2020)] that three families of highly symmetric states are many-body scars for any spin-1/2 fermionic Hamiltonian of the form H-0 + OT, where T is a generator of an appropriate Lie group. One of these families consists of the well-known eta-pairing states. In addition to having the usual properties of scars, these families of states are insensitive to electromagnetic noise and have advantages for storing and processing quantum information. In this paper we show that a number of well-known coupling terms, such as the Hubbard and the Heisenberg interactions, and the Hamiltonians containing them, are of the required form and support these states as scars without fine tuning. The explicit H-0 + OT decomposition for a number of most commonly used models, including topological ones, is provided. To facilitate possible experimental implementations, we discuss the conditions for the low-energy subspace of these models to be comprised solely of scars. Further, we write all the generators T that can be used as building blocks for designing new models with scars, most interestingly including the spin-orbit coupled hopping and superconducting pairing terms. We expand this framework to the non-Hermitian open systems and demonstrate that for them the scar subspace continues to undergo coherent time evolution and exhibit the revivals. A full numerical study of an extended two-dimensional tJU model explicitly illustrates the novel properties of the invariant scars and supports our findings.

Automated summary

The research shows that three highly symmetric families of states are many-body scars for certain forms of fermionic Hamiltonians, with one of them being the well-known eta-pairing states. These states, besides possessing typical scar properties, are also insensitive to electromagnetic noise and advantageous for quantum information storage and processing. Additionally, various common coupling terms and the Hamiltonians containing them support these states as scars without requiring fine-tuning.