Many-Body Scars as a Group Invariant Sector of Hilbert Space
Abstract
We present a class of Hamiltonians H for which a sector of the Hilbert space invariant under a Lie group G, which is not a symmetry of H, possesses the essential properties of many-body scar states. These include the absence of thermalization and the “revivals” of special initial states in time evolution. Here, a particular class of examples concerns interacting spin-1/2 fermions on a lattice consisting of N sites (it includes deformations of the Fermi-Hubbard model as special cases), and we show that it contains two families of N + 1 scar states. One of these families, which was found in recent literature, comprises the well-known η-pairing states. We find another family of scar states that is U(N) invariant. Both families and most of the group-invariant scar states produced by our construction, in general, give rise to the off-diagonal long range order, which survives at high temperatures and is insensitive to the details of the dynamics. Such states could be used for reliable quantum information processing because the information is stored nonlocally and thus cannot be easily erased by local perturbations. In contrast, other scar states we find are product states, which could be easily prepared experimentally. The dimension ofmore »
- Publication Date:
- Research Org.:
- Princeton Univ., NJ (United States)
- Sponsoring Org.:
- USDOE; National Science Foundation (NSF)
- OSTI Identifier:
- 1729852
- Grant/Contract Number:
- SC0002140; PHY-1620059; PHY-1914860
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 125; Journal Issue: 23; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Eigenstate thermalization; Entanglement entropy; Quantum correlations in quantum information; Quantum entanglement; Quantum information processing; Quantum nonlocality; Quantum quench; Quantum statistical mechanics; Superconductivity
Citation Formats
Pakrouski, K., Pallegar, P. N., Popov, F. K., and Klebanov, I. R. Many-Body Scars as a Group Invariant Sector of Hilbert Space. United States: N. p., 2020.
Web. doi:10.1103/physrevlett.125.230602.
Pakrouski, K., Pallegar, P. N., Popov, F. K., & Klebanov, I. R. Many-Body Scars as a Group Invariant Sector of Hilbert Space. United States. https://doi.org/10.1103/physrevlett.125.230602
Pakrouski, K., Pallegar, P. N., Popov, F. K., and Klebanov, I. R. Tue .
"Many-Body Scars as a Group Invariant Sector of Hilbert Space". United States. https://doi.org/10.1103/physrevlett.125.230602. https://www.osti.gov/servlets/purl/1729852.
@article{osti_1729852,
title = {Many-Body Scars as a Group Invariant Sector of Hilbert Space},
author = {Pakrouski, K. and Pallegar, P. N. and Popov, F. K. and Klebanov, I. R.},
abstractNote = {We present a class of Hamiltonians H for which a sector of the Hilbert space invariant under a Lie group G, which is not a symmetry of H, possesses the essential properties of many-body scar states. These include the absence of thermalization and the “revivals” of special initial states in time evolution. Here, a particular class of examples concerns interacting spin-1/2 fermions on a lattice consisting of N sites (it includes deformations of the Fermi-Hubbard model as special cases), and we show that it contains two families of N + 1 scar states. One of these families, which was found in recent literature, comprises the well-known η-pairing states. We find another family of scar states that is U(N) invariant. Both families and most of the group-invariant scar states produced by our construction, in general, give rise to the off-diagonal long range order, which survives at high temperatures and is insensitive to the details of the dynamics. Such states could be used for reliable quantum information processing because the information is stored nonlocally and thus cannot be easily erased by local perturbations. In contrast, other scar states we find are product states, which could be easily prepared experimentally. The dimension of scar subspace is directly controlled by the choice of group G and can be made exponentially large.},
doi = {10.1103/physrevlett.125.230602},
journal = {Physical Review Letters},
number = 23,
volume = 125,
place = {United States},
year = {2020},
month = {12}
}
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