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Large classes of quantum scarred Hamiltonians from matrix product states

Journal Article · · Physical Review. B
 [1];  [2];  [3];  [4];  [5]
  1. Princeton Univ., NJ (United States); OSTI
  2. Univ. of Oxford (United Kingdom). Clarendon Lab.
  3. Princeton Univ., NJ (United States)
  4. Univ. of Oxford (United Kingdom). Clarendon Lab.; All Souls College, Oxford (United Kingdom)
  5. Princeton Univ., NJ (United States); Ecole Normale Supérieure (ENS), Paris (France); Université PSL, Paris (France); Centre National de la Recherche Scientifique (CNRS), Paris (France); Sorbonne Univ., Paris (France); Université Paris-Diderot (France); Sorbonne Paris Cité (France)
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Motivated by the existence of exact many-body quantum scars in the Affleck-Kennedy-Lieb-Tasaki (AKLT) chain, in this work we explore the connection between matrix product state (MPS) wave functions and many-body quantum scarred Hamiltonians. We provide a method to systematically search for and construct parent Hamiltonians with towers of exact eigenstates composed of quasiparticles on top of an MPS wave function. These exact eigenstates have low entanglement in spite of being in the middle of the spectrum, thus violating the strong eigenstate thermalization hypothesis. Using our approach, we recover the AKLT chain starting from the MPS of its ground state, and we derive the most general nearest-neighbor Hamiltonian that shares the AKLT quasiparticle tower of exact eigenstates. We further apply this formalism to other simple MPS wave functions, and derive families of Hamiltonians that exhibit AKLT-like quantum scars. As a consequence, we also construct a scar-preserving deformation that connects the AKLT chain to the integrable spin-1 pure biquadratic model. Finally, we also derive other families of Hamiltonians that exhibit types of exact quantum scars, including a $$\textit{U}$$(1)-invariant perturbed Potts model.

Research Organization:
Princeton Univ., NJ (United States)
Sponsoring Organization:
USDOE Office of Science (SC); Packard Foundation; National Science Foundation (NSF); Engineering and Physical Sciences Research Council (EPSRC)
Grant/Contract Number:
SC0016239
OSTI ID:
1802874
Journal Information:
Physical Review. B, Journal Name: Physical Review. B Journal Issue: 8 Vol. 102; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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