Asymptotic Quantum Many-Body Scars
Abstract
We consider a quantum lattice spin model featuring exact quasiparticle towers of eigenstates with low entanglement at finite size, known as quantum many-body scars (QMBS). We show that the states in the neighboring part of the energy spectrum can be superposed to construct entire families of low-entanglement states whose energy variance decreases asymptotically to zero as the lattice size is increased. As a consequence, they have a relaxation time that diverges in the thermodynamic limit, and therefore exhibit the typical behavior of exact QMBS, although they are not exact eigenstates of the Hamiltonian for any finite size. We refer to such states as asymptotic QMBS. These states are orthogonal to any exact QMBS at any finite size, and their existence shows that the presence of an exact QMBS leaves important signatures of nonthermalness in the rest of the spectrum; therefore, QMBS-like phenomena can hide in what is typically considered the thermal part of the spectrum. We support our study using numerical simulations in the spin-1 XY model, a paradigmatic model for QMBS, and we conclude by presenting a weak perturbation of the model that destroys the exact QMBS while keeping the asymptotic QMBS.
Copyright and License
© 2023 American Physical Society.
Acknowledgement
We warmly acknowledge enlightening discussions with Saverio Bocini, Xiangyu Cao, Maurizio Fagotti, David Huse, Michael Knap, Lesik Motrunich, and Nicolas Regnault. We also thank Lesik Motrunich for useful comments on a draft. L. G. and L. M. also thank Guillaume Roux and Pascal Simon for discussions on previous shared projects. This work is supported by the Walter Burke Institute for Theoretical Physics at Caltech and the Institute for Quantum Information and Matter, by LabEx PALM (ANR-10-LABX-0039-PALM) in Orsay, by Region Ile-de-France in the framework of the DIM Sirteq and by the Swiss National Science Foundation under Division II (Grant No. 2000020-188687). S. M. also acknowledges the hospitality of the Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS) in Orsay, where this collaboration was initiated, and the Physik-Insitut of the University of Zurich, where some of this work was performed.
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Additional details
- ISSN
- 1079-7114
- Walter Burke Institute for Theoretical Physics
- Institute for Quantum Information and Matter, California Institute of Technology
- Agence Nationale de la Recherche
- ANR-10-LABX-0039-PALM
- Swiss National Science Foundation
- 2000020-188687
- Caltech groups
- Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics