Granovskii-Zhedanov Scar of XYZ Spin-chain: Modern Algebraic Perspectives and Realization in Higher Dimensional Lattices

• URL: http://arxiv.org/abs/2507.14895v1
• Date: Sun, 20 Jul 2025 10:20:15 GMT
• Title: Granovskii-Zhedanov Scar of XYZ Spin-chain: Modern Algebraic Perspectives and Realization in Higher Dimensional Lattices
• Authors: Dhiman Bhowmick, Wen Wei Ho,
• Abstract summary: We uncover the origin of the Granovskii-Zhedanov (GZ) scar within the framework of the modern understanding of quantum many-body scars.<n>We explore the possibility of constructing lattice-independent GZ scars in higher-dimensional uniform spin-exchange systems with centrosymmetry.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In a work by Granovskii and Zhedanov, a surprising scar state exhibiting zero entanglement and long periodicity was discovered in the XYZ spin chains; remarkably, nearly three decades before the concept of many-body scars became a subject of active research. In this study, we uncover the origin of the Granovskii-Zhedanov (GZ) scar within the framework of the modern understanding of quantum many-body scars. We demonstrate that the scar subspace can be effectively described using the standard spectrum-generating algebra (SGA) framework and through a group-theoretical formulation of the Hamiltonian. This description, however, is applicable only in the XXZ limit, where a quasi-$U(1)$ symmetry exists within the scar subspace. In contrast, the absence of such quasi-$U(1)$ symmetry for the GZ scar subspace restricts the applicability of these standard formulations. We propose two alternative techniques: approximated SGA and generalized SGA, which construct and describe the scar subspace in the XYZ case. Using these approaches, we can characterize the scar subspaces. We further explore the possibility of constructing lattice-independent GZ scars in higher-dimensional uniform spin-exchange systems with centrosymmetry, using graphical rules developed for GZ scar construction. Our results indicate that lattice-independent GZ scars cannot be supported on uniform lattices with odd coordination numbers or plaquettes with an odd number of edges, while uniform lattices featuring even coordination numbers and even-edged plaquettes can host such lattice-independent scars in specific scenarios. Remarkably, if certain bonds retain the full $SU(2)$ symmetry of the spin-exchange interaction, thereby breaking the spatial uniformity of the lattice, lattice-independent GZ scars can still emerge in systems with odd coordination numbers or plaquettes with an odd number of edges.

Related papers

• Hidden $Z_{2}\ imes Z_{2}$ subspace symmetry protection for quantum scars [0.0]
  We study the paradigmatic spin-1 XY chain under open boundary conditions, which hosts exact quantum many-body scars generated by an emergent Spectrum Generating Algebra (SGA)<n>We show that the scar subspace possesses a symmetry-protected trivial (SPt) character that we attribute to a hidden $Z_2times Z_2$ symmetry of another model, namely the commutant Hamiltonian.<n>A complementary understanding of the stability of the scars under different perturbations is obtained by analyzing the Loschmidt echo and Quantum Fisher Information (QFI) of the scars.
  arXiv  Detail & Related papers  (2026-02-25T20:47:26Z)
• Asymmetric decay of quantum many-body scars in XYZ quantum spin chains [0.0]
  Quantum many-body scars are atypical energy eigenstates of chaotic quantum many-body systems.<n>Scars arise in the form of an infinite family of highly excited yet nonentangled product-state eigenstates.
  arXiv  Detail & Related papers  (2025-05-08T17:23:34Z)
• Critical spin models from holographic disorder [49.1574468325115]
  We study the behavior of XXZ spin chains with a quasiperiodic disorder not present in continuum holography.<n>Our results suggest the existence of a class of critical phases whose symmetries are derived from models of discrete holography.
  arXiv  Detail & Related papers  (2024-09-25T18:00:02Z)
• Fractionalization paves the way to local projector embeddings of quantum many-body scars [0.0]
  We show how to fit the Affleck-Kennedy-Lieb-Tasaki (AKLT) model or the PXP model of Rydberg-blockaded atoms. The embedding of the original system in a larger space elucidates the structure of their scar states and simplifies their construction.
  arXiv  Detail & Related papers  (2023-05-01T13:55:41Z)
• Duality between open systems and closed bilayer systems, and thermofield double states as quantum many-body scars [49.1574468325115]
  We find a duality between open many-body systems governed by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. Under this duality, the identity operator on the open system side maps to the thermofield double state. We identify broad classes of many-body open systems with nontrivial explicit eigen operators $Q$ of the Lindbladian superoperator.
  arXiv  Detail & Related papers  (2023-04-06T15:38:53Z)
• Quantum many-body scars in bipartite Rydberg arrays originate from hidden projector embedding [0.0]
  We study the ergodicity-breaking "quantum many-body scar" states that appear in the PXP model describing constrained Rabi oscillations. For a wide class of bipartite lattices of Rydberg atoms, we reveal that the nearly energy-equidistant tower of these states arises from the Hamiltonian's close proximity to a generalized projector-embedding form.
  arXiv  Detail & Related papers  (2022-03-01T18:06:53Z)
• Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry [85.36456486475119]
  A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
  arXiv  Detail & Related papers  (2021-11-24T15:50:22Z)
• Group theoretic approach to many-body scar states in fermionic lattice models [0.0]
  We show that three families of highly symmetric states are many-body scars for any spin-1/2 fermionic Hamiltonian. We write down all the generators $T$ that can be used as building blocks for designing new models with scars. A full numerical study of an extended 2D $tJU$ model explicitly illustrates the novel properties of the invariant scars.
  arXiv  Detail & Related papers  (2021-06-18T18:06:06Z)
• Disorder enhanced quantum many-body scars in Hilbert crystals [0.0]
  We consider a model arising in facilitated Rydberg chains with positional disorder which features a Hilbert space with the topology of a $d$-dimensional hypercube. We show that an integrability-breaking disorder enhances the scars followed by inhibition of the dynamics due to strong localization of the eigenstates in the large disorder limit. Next, mapping the model to the spin-1/2 XX Heisenberg chain offers a simple geometrical perspective on the recently proposed Onsager scars.
  arXiv  Detail & Related papers  (2020-12-09T20:42:13Z)
• Exact many-body scars and their stability in constrained quantum chains [55.41644538483948]
  Quantum scars are non-thermal eigenstates characterized by low entanglement entropy. We study the response of these exact quantum scars to perturbations by analysing the scaling of the fidelity susceptibility with system size.
  arXiv  Detail & Related papers  (2020-11-16T19:05:50Z)
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics [58.720142291102135]
  We propose quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions. We show that our system exhibits topologicalband structures under appropriate conditions.
  arXiv  Detail & Related papers  (2020-08-06T19:58:05Z)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)
• Multidimensional dark space and its underlying symmetries: towards dissipation-protected qubits [62.997667081978825]
  We show that a controlled interaction with the environment may help to create a state, dubbed as em dark'', which is immune to decoherence. To encode quantum information in the dark states, they need to span a space with a dimensionality larger than one, so different states act as a computational basis. This approach offers new possibilities for storing, protecting and manipulating quantum information in open systems.
  arXiv  Detail & Related papers  (2020-02-01T15:57:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.