Theory of robust quantum many-body scars in long-range interacting
systems
- URL: http://arxiv.org/abs/2309.12504v2
- Date: Mon, 30 Oct 2023 19:00:18 GMT
- Title: Theory of robust quantum many-body scars in long-range interacting
systems
- Authors: Alessio Lerose, Tommaso Parolini, Rosario Fazio, Dmitry A. Abanin,
Silvia Pappalardi
- Abstract summary: Quantum many-body scars (QMBS) are exceptional energy eigenstates of quantum many-body systems.
We show that the setting of long-range interacting quantum spin systems generically hosts robust QMBS.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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
the setting of long-range interacting quantum spin systems generically hosts
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 exactly solve for the eigenstates of this interacting
impurity model, and show their self-consistent localization in large-spin
sectors of the original Hamiltonian for $0<\alpha<d$. 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. Broader perspectives of this work range
from independent applications of the technical toolbox developed here to
informing experimental routes to metrologically useful multipartite
entanglement.
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