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

TL;DR

This paper uncovers a new class of exactly stabilizer-structured eigenstates, called sublattice scars, in a 2D $U(1)$ lattice gauge theory, linking quantum many-body scars to stabilizer states and enabling efficient classical simulation.

Contribution

It introduces sublattice scars as a novel class of exact stabilizer eigenstates in a 2D lattice gauge model, connecting quantum scars to stabilizer quantum information.

Findings

Identification of sublattice scars from gauge-invariant zero modes.

These scars form an intrinsic stabilizer manifold within the spectrum.

Explicit Clifford circuits are constructed to prepare these states.

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 R\'enyi 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.