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Systematic construction of asymptotic quantum many-body scar states and their relation to supersymmetric quantum mechanics

Masaya Kunimi1,*, Yusuke Kato2,3,†, and Hosho Katsura4,5,6,‡

  • *Contact author: kunimi@rs.tus.ac.jp
  • †Contact author: yusuke@phys.c.u-tokyo.ac.jp
  • ‡Contact author: katsura@phys.s.u-tokyo.ac.jp
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Phys. Rev. Research 7, 043107 – Published 27 October, 2025

DOI: https://doi.org/10.1103/zstl-s1y2

Abstract

We develop a systematic method for constructing asymptotic quantum many-body scar (AQMBS) states. While AQMBS states are closely related to quantum many-body scar (QMBS) states, they exhibit key differences. Unlike QMBS states, AQMBS states are not energy eigenstates of the Hamiltonian, making their construction more challenging. We demonstrate that, under appropriate conditions, AQMBS states can be obtained as low-lying gapless excited states of a parent Hamiltonian, which has a QMBS state as its ground state. Furthermore, our formalism reveals a connection between QMBS and supersymmetric (SUSY) quantum mechanics. The QMBS state can be interpreted as a SUSY-unbroken ground state.

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Physics Subject Headings (PhySH)

Corrections

15 December, 2025

Correction: In the summation in Eq. (75), ∑n=1M−n has been changed to ∑j=1M−n.

11 February, 2026

Second Correction: In Eq. (112), the first term has been changed from P̂ĤXYS=1/2P̂ to P̂(ĤXYS=1/2)2P̂.

Article Text

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Phys. Rev. Research 7, 043107– Published 27 October, 2025
  • Received 21 May 2025
  • Accepted 22 September 2025
  • Corrected 15 December 2025
  • Corrected 11 February 2026
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