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

TL;DR

This paper develops a group theoretic framework to identify and construct many-body scar states in fermionic lattice models, including well-known and new models, with potential for quantum information applications and experimental realization.

Contribution

It provides an explicit $H_0+OT$ decomposition for common models, identifies all generators for scar construction, and extends the framework to non-Hermitian systems.

Findings

Certain coupling terms support scar states without fine-tuning.

Explicit decompositions for models including topological ones are provided.

Scar states exhibit coherent revivals even in open non-Hermitian systems.

Abstract

It has been shown [arXiv:2007.00845] 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 down 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 2D $tJU$ model explicitly illustrates the novel properties of the invariant scars and supports our findings.