Many Body Scars as a Group Invariant Sector of Hilbert Space

TL;DR

This paper introduces a class of Hamiltonians with group-invariant sectors that exhibit many-body scar states, characterized by non-thermalization, revivals, and potential applications in quantum information storage, extending previous scar state concepts.

Contribution

The authors construct Hamiltonians with group-invariant sectors hosting scar states, including new families with specific invariance properties, broadening the understanding of many-body scars beyond prior models.

Findings

Identified two families of scar states in spin-1/2 fermion models.

Demonstrated that scar states exhibit off-diagonal long-range order at high temperatures.

Showed the scar subspace dimension can be exponentially large, depending on the group G.

Abstract

We present a class of Hamiltonians $H$ for which a sector of the Hilbert space invariant under a Lie group $G$, which is not a symmetry of $H$, possesses the essential properties of many-body scar states. These include the absence of thermalization and the "revivals" of special initial states in time evolution. Some of the scar states found in earlier work may be viewed as special cases of our construction. A particular class of examples concerns interacting spin-1/2 fermions on a lattice consisting of $N$ sites (it includes deformations of the Fermi-Hubbard model as special cases), and we show that it contains two families of $N+1$ scar states. One of these families, which was found in recent literature, is comprised of the well-known $\eta$-pairing states. We find another family of scar states which is $U(N)$ invariant. Both families and most of the group-invariant scar states produced by our construction in general, give rise to the off-diagonal long range order which survives at high temperatures and is insensitive to the details of the dynamics. Such states could be used for reliable quantum information processing because the information is stored non-locally, and thus cannot be easily erased by local perturbations. In contrast, other scar states we find are product states which could be easily prepared experimentally. The dimension of scar subspace is directly controlled by the choice of group $G$ and can be made exponentially large.