Scar subspaces stabilized by algebraic closure: Beyond equally-spaced spectra and exact solvability

TL;DR

This paper introduces a new class of quantum many-body systems with an $$-invariant scar subspace, characterized by algebraic closure, leading to complex spectral structures and multifrequency revivals beyond traditional models.

Contribution

It extends the quantum many-body scar paradigm by constructing systems with algebraic closure, resulting in non-equidistant spectra and robust scar subspaces without requiring exact eigenstate solvability.

Findings

Spectrum forms a multidirectional lattice structure.

System exhibits multifrequency oscillations.

Scar subspace remains stable under perturbations.

Abstract

We construct a class of quantum many-body systems hosting an $\mathfrak{su}(3)$-invariant scar subspace, extending the conventional paradigm of quantum many-body scars beyond equally spaced spectra and single-directional tower structures. Our construction is based on local constraints that realize an algebraic closure within the scar subspace. As a result, the spectrum in the subspace is no longer equally spaced, but instead forms a multidirectional lattice structure parametrized by multiple independent quantum numbers. This leads to qualitatively new dynamical signatures: instead of single-frequency revivals, the system exhibits multifrequency oscillations governed by integer linear combinations of distinct energy scales. Importantly, the stability of the scar subspace does not rely on exact solvability of individual eigenstates. We show that algebraic closure preserves the invariant subspace even under perturbations that render the eigenstates analytically intractable, thereby realizing quantum many-body scars on an unsolvable reference state. Our results identify algebraic closure as a unifying mechanism underlying scar subspaces beyond the conventional $\mathfrak{su}(2)$ paradigm, and open a route toward richer nonthermal dynamics in nonintegrable quantum systems.