Exact stabilizer scars in two-dimensional $U(1)$ lattice gauge theory

Abstract

The complexity of highly excited eigenstates is a central theme in nonequilibrium many-body physics, underpining questions of thermalization, classical simulability, and quantum information structure. In this work, considering the paradigmatic Rokhsar-Kivelson model, we connect quantum many-body scarring in Abelian lattice gauge theories to an emergent stabilizer structure. We identify a distinct class of scarred eigenstates, termed sublattice scars, originating from gauge-invariant zero modes that form exact stabilizer states. Remarkably, although the underlying Hamiltonian is not a stabilizer Hamiltonian, its eigenspectrum intrinsically hosts exact stabilizer eigenstates. These sublattice scars exhibit vanishing stabilizer Rényi entropy together with finite, highly structured entanglement, enabling efficient classical simulation. Exploiting their stabilizer structure, we construct explicit Clifford circuits that prepare these states in a two-dimensional lattice gauge model. Our results demonstrate that the scarred subspace of the Rokhsar-Kivelson spectrum forms an intrinsic stabilizer manifold, revealing a direct connection between stabilizer quantum information, lattice gauge constraints, and quantum many-body scarring.

Figures (7)

• Figure 1: Schematic representation of the RK Hamiltonian: action of $(i)$$O_{\mathrm{kin}}$$(ii)$$O_{\mathrm{pot}}$ operators on active/flippable plaquettes.
• Figure 2: $(i) -(ii)$ Stabilizer sublattice scars in a $2\times2$ RK model with PBC in the energy sector $E=2$. These states possess $M_2 = 0$, $S_{\mathrm{vN}} = \ln 2$ and $\mathcal{O}_{\mathrm{kin}} = 0$, and exhibit $\mathcal{O}_{\mathrm{pot},\square} = 1$ on plaquettes belonging to one sublattice and $0$ on the complementary one.
• Figure 3: $(i)$ Stabilizer Rényi entropy $M_2$, $(ii)$ bipartite entanglement entropy $S_{vN}$, and $(iii)$ multifractal flatness $\tilde{F}$ across the eigenspectrum for the $4\times2$ plaquette system with PBC. In $(i)$, two sublattice stabilizer scars at $E=4$ exhibit vanishing $M_2$, with trivial Fock stabilizer states marked in green and nontrivial sublattice stabilizer scars marked in red. In $(ii)$, the Fock states show $S_{\mathrm{vN}}=0$ owing to their product-state nature, while the sublattice stabilizer scars display finite entanglement $S_{\mathrm{vN}}=2\times \ln 2$. Panel $(iii)$ shows the multifractal flatness, where states at $E=2$ and $E=8$ appear flat but do not correspond to valid stabilizer states, consistent with the absence in $(i)$ of $M_2=0$ states at $E=2$ and $8$.
• Figure 4: $(i)$ Multifractal flatness, $(ii)$ bipartite entanglement entropy, across the eigenspectrum for the $4\times4$ plaquette system with periodic boundary conditions.
• Figure 5: Sketch of the general structure of stabilizer sublattice scars. Green (white) plaquettes are active (inactive). The plaquettes linked by a purple rod formed a dimer in a singlet state.