Exact Quantum Many-Body Scars in 2D Quantum Gauge Models

TL;DR

The work demonstrates exact QMBS in a 2D spin-1/2 XY model with a transverse field and shows these scars persist under a generalized Kramers-Wannier duality as scars in a dual $$ lattice gauge theory. Scar states are constructed from stripe (and hexagon-centered) excitations, forming a tower with energies offset by multiples of the field and exhibiting area-law entanglement despite residing in the middle of the spectrum. The duality framework extends the scar construction to honeycomb/triangular and kagome/dice lattices, preserves scar structure under correlated disorder and inhomogeneous fields, and reveals how gauging a global symmetry maps QMBS to gauge-theoretic contexts. This provides a versatile, geometrically broad method for locating QMBS in higher dimensions and connects QMBS to non-invertible/categorical symmetries, with potential experimental realizations in ultracold-atom or superconducting-qubit platforms.

Abstract

Quantum many-body scars (QMBS) serve as important examples of ergodicity-breaking phenomena in quantum many-body systems. Despite recent extensive studies, exact QMBS are rare in dimensions higher than one. In this paper, we study a two-dimensional quantum $\mathbb{Z}_2$ gauge model that is dual to a two-dimensional spin-$1/2$ XY model defined on bipartite graphs. We identify the exact eigenstates of the XY model with a tower structure as exact QMBS. Exploiting the duality transformation, we show that the exact QMBS of the XY model (and XXZ model) after the transformation are the exact QMBS of the dual $\mathbb{Z}_2$ gauge model. This construction is versatile and has potential applications for finding new QMBS in other higher-dimensional models.

Figures (19)

• Figure 1: Tilted square lattice where the XY model is defined. Spin-$\frac{1}{2}$s are located at the vertices, with the total number of spins being $2 L_x L_y$ in the periodic boundary case. In this figure, we have $L_x=4$ and $L_y=4$. With open boundaries in both directions, the total number of spins is $2L_x L_y +L_x +L_y$. We use red and blue colors to denote a bipartition of the tilted square lattice, which are used in Sec. \ref{['subsec:QMBSsquare']}.
• Figure 2: We consider a staggered superposition of single up spin, taken from the stripe $S$ shown in this figure. The relative signs are expressed in red color.
• Figure 3: When $\mathbf{H}_{\rm XY}$ moves around the up spin, the two contributions from nearby sites cancel out, thanks to the staggered choice of the relative signs in \ref{['eq:S']}. This is a two-dimensional generalization of the one-dimensional counterpart shown in \ref{['fig:1d_scar_cancel']} in \ref{['app:1d']}.
• Figure 4: We can consider multiple stripes $S, S', \dots$, to obtain a collection of eigenstates. The number of such stripes can grow as $O(L)$ for the linear system size $L$.
• Figure 5: The cancelation mechanism fails when we have a bending strip. This means only straight stripes are allowed.