Abstract
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-$\frac{1}{2}$ 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 $\ensuremath{\eta}$-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.
Highlights
In our previous paper [22], we presented a general strategy for systematically designing the Hamiltonians with a many-body scar subspace S invariant under the action of a continuous group G, which is bigger than the symmetry group of the Hamiltonian
A closed SO(N ) algebra is formed by the “even” long-range real-amplitude hopping that contains exclusively the terms connecting the sites belonging to different groups of the bipartite lattice in Fig. 2, meaning that it is a hopping over 2k neighbors, where k is a non-negative integer
We have shown explicitly that the Hamiltonians of some well-known models (Table III) are of the H0 + OT form; they support the group-invariant scars for any coupling constants and without a need for fine tuning
Summary
In recent literature there has been considerable interest in the many-body scar states [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37] (for their pedagogical overviews, see [38,39]). Examples of many-body scars have been found in a number of systems including correlated electron models with the Heisenberg [12,18,43,44], Hubbard [11,18,20,45] and density-density [46,47] interactions. We demonstrate that many of the commonly used condensed matter models of interacting electrons happen to be of this form and specify their group-invariant scar subspaces S This applies to the Hubbard, Heisenberg, and some other interactions, and any models constructed out of them on various lattices and in arbitrary dimension such as the extended two-dimensional (2D) tJU model that we consider in detail as a prototype. V) where the full construction is detailed for the tJU model and the numerical evidence of many-body scar states is provided
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