TY - JOUR

T1 - Many-Body Scars as a Group Invariant Sector of Hilbert Space

AU - Pakrouski, K.

AU - Pallegar, P. N.

AU - Popov, F. K.

AU - Klebanov, I. R.

N1 - Funding Information:
We are grateful to A. Prem, D. Abanin, A. Bernevig, D. Calugaru, A. Dymarsky, M. Gullans, A. Milekhin, S. Moudgalya, and G. Tarnopolsky for valuable discussions. We also thank A. Bernevig, S. Moudgalya, and B. Buča for comments on a draft of this Letter. The simulations presented in this Letter were performed on computational resources managed and supported by Princeton’s Institute for Computational Science and Engineering and OIT Research Computing. This research was supported in part by the U.S. NSF under Grants No. PHY-1620059 and No. PHY-1914860. K. P. was also supported by the Swiss National Science Foundation through the Early Postdoc.Mobility Grant No. P2EZP2_172168 and by DOE Award No. de-sc0002140.

PY - 2020/12/1

Y1 - 2020/12/1

N2 - 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. 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.

AB - 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. 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.

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U2 - 10.1103/PhysRevLett.125.230602

DO - 10.1103/PhysRevLett.125.230602

M3 - Article

AN - SCOPUS:85097587249

VL - 125

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 23

M1 - 230602

ER -