Parent Hamiltonians for stabilizer quantum many-body scars

TL;DR

This paper introduces a systematic method to construct local Hamiltonians with stabilizer quantum many-body scars as exact eigenstates, unifying previous results and enabling new complex entangled scar states.

Contribution

A general framework for embedding stabilizer states as QMBS in local Hamiltonians using factorizability of Pauli strings, unifying and extending prior constructions.

Findings

Reproduces known volume-law entangled QMBS like rainbow states

Constructs new stabilizer QMBS with complex entanglement structures

Exact diagonalization confirms stabilizer states as eigenstates of parent Hamiltonians

Abstract

Quantum many-body scars (QMBS) have attracted considerable interest due to their role in weak ergodicity breaking in many-body systems. We present a general construction that embeds stabilizer states as QMBS of local Hamiltonians. The method relies on a notion of factorizability of Pauli strings on a lattice, which is used to convert stabilizer elements into local, few-body operators that annihilate the stabilizer state. This enables the systematic construction of parent Hamiltonians with zero-energy stabilizer QMBS typically near the middle of the spectrum. The method reproduces several known results in a unified framework, including recent examples of volume-law entangled QMBS, such as the ``rainbow'' QMBS and the entangled antipodal Bell pair state. We also apply the framework to construct examples of stabilizer QMBS with a more complex entanglement structure, such as the cluster state, the toric code state, and a volume-law entangled state we dub the antipodal toric code (ATC) state. Exact diagonalization confirms our results and reveal the stabilizer states as exact eigenstates of their parent Hamiltonian.