Theory of robust quantum many-body scars in long-range interacting systems

TL;DR

This paper demonstrates that long-range interacting quantum spin systems naturally host robust quantum many-body scars, providing an analytical framework to understand their stability and breakdown, with implications for thermalization and Floquet dynamics.

Contribution

The authors develop an analytical approach mapping the spin Hamiltonian to a relativistic quantum rotor coupled to bosonic modes, revealing the stability mechanism of QMBS in long-range systems.

Findings

Spectral signatures of chaos appear for infinitesimal decay exponent $oldsymbol{ extalpha}$, but QMBS features persist.

Analytical solution via a polaron-type transformation shows localization of eigenstates in large-spin sectors.

Predictive criterion for heating under periodic driving in long-range systems is established.

Abstract

Quantum many-body scars (QMBS) are exceptional energy eigenstates of quantum many-body systems associated with violations of thermalization for special non-equilibrium initial states. Their various systematic constructions require fine-tuning of local Hamiltonian parameters. In this work we demonstrate that long-range interacting quantum spin systems generically host robust QMBS. We analyze spectral properties upon raising the power-law decay exponent $\alpha$ of spin-spin interactions from the solvable permutationally-symmetric limit $\alpha=0$. First, we numerically establish that despite spectral signatures of chaos appear for infinitesimal $\alpha$, the towers of $\alpha=0$ energy eigenstates with large collective spin are smoothly deformed as $\alpha$ is increased, and exhibit characteristic QMBS features. To elucidate the nature and fate of these states in larger systems, we introduce an analytical approach based on mapping the spin Hamiltonian onto a relativistic quantum rotor non-linearly coupled to an extensive set of bosonic modes. We analitycally solve for the eigenstates of this interacting impurity model by means of a novel polaron-type canonical transformation, and show their self-consistent localization in large-spin sectors of the original Hamiltonian for $0<\alpha<d$ (with $d$ = spatial dimension of the lattice). Our theory unveils the stability mechanism of such QMBS for arbitrary system size and predicts instances of its breakdown, e.g. near dynamical critical points or in presence of semiclassical chaos, which we verify numerically in long-range quantum Ising chains. As a byproduct, we find a predictive criterion for presence or absence of heating under periodic driving for $0<\alpha<d$, beyond existing Floquet-prethermalization theorems.