Quantum scars as embeddings of weakly broken Lie algebra representations

Abstract

We present an interpretation of scar states and quantum revivals as weakly "broken" representations of Lie algebras spanned by a subset of eigenstates of a many-body quantum system. We show that the PXP model, describing strongly-interacting Rydberg atoms, supports a "loose" embedding of multiple su(2) Lie algebras corresponding to distinct families of scarred eigenstates. Moreover, we demonstrate that these embeddings can be made progressively more accurate via an iterative process which results in optimal perturbations that stabilize revivals from arbitrary charge density wave product states, |Zn , including ones that show no revivals in the unperturbed PXP model. We discuss the relation between the loose embeddings of Lie algebras present in the PXP model and recent exact constructions of scarred states in related models. arXiv:2001.08232v1 [cond-mat.str-el]

Quantum many-body scars and weak breaking of ergodicity

“…In principle, using this construction, one could form the Casimir operator for the su(2) algebra and obtain the tower of non-thermal eigenstates by acting repeatedly with H + on the ground state of the Casimir, mirroring the general procedure outlined previously. However, this procedure is not analytically tractable due to the fact that the ground state of the Casimir operator is not known and the algebra of the PXP model is only approximate (recent works, however, have shown that weak deformations of the PXP model make the algebra and dynamical revivals progressively more accurate [58][59][60]). Instead, different schemes have been used to approximate scarred eigenstates in the PXP model starting from |Z 2 product state [16,61].…”

Proposal for Realizing Quantum Scars in the Tilted 1D Fermi-Hubbard Model

“…In this case, the particle's eigenfuctions exhibit anomalous concentration in the vicinity of an unstable periodic orbit in the classical limit → 0 [40][41][42], leading to observable conse-quences in many physical systems [43][44][45][46]. In recent experiments on interacting Rydberg atom arrays [47], weak ergodicity breaking was observed via persistent revivals following the global quench of the system, prompting the name "quantum many-body scarring" [48][49][50] by analogy with stadium billiards [51,52]. Recently, quantum many-body scarring has been shown to occur in higher dimensions [53][54][55] and in the presence of certain kinds of perturbations [56][57][58] including disorder [59].…”

η -pairing states as true scars in an extended Hubbard model

“…The experiment is modeled by the "PXP model" [13,14]. While there are several approximate ways of understanding the scar states in the PXP model [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], only some eigenstates in the middle of the spectrum are known exactly [17,21].…”