Stabilization of Granovskii-Zhedanov scars of the XYZ quantum spin chain via non-Hermitian spin relaxation

• URL: http://arxiv.org/abs/2606.01254v1
• Date: Sun, 31 May 2026 14:18:17 GMT
• Title: Stabilization of Granovskii-Zhedanov scars of the XYZ quantum spin chain via non-Hermitian spin relaxation
• Abstract summary: Granovskii-Zhedanov (GZ) states are exact scar states of the spin-S XYZ chain for S >= 1.<n>We study the stability and dynamics of GZ states in the presence of generic perturbations.<n>We show that the inclusion of effective non-Hermitian spin relaxation processes can substantially stabilize the GZ states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Granovskii-Zhedanov (GZ) states are exact scar states of the spin-S XYZ chain for S >= 1. As a result, local quantum information encoded in a GZ state remains preserved under the unitary dynamics of the XYZ Hamiltonian; thus, these states evade thermalization and violate ergodicity despite the system being otherwise nonintegrable and chaotic. However, in realistic experimental settings, the realization of an ideal XYZ Hamiltonian is not possible, as perturbations are inevitable. These perturbations ultimately lead to the decay and thermalization of the GZ state. We study the stability and dynamics of GZ states in the presence of generic perturbations and propose physically realistic mechanisms to stabilize them. We show that the product structure of the GZ state allows its lifetime to be enhanced in the presence of an external helical magnetic field, which slows down thermalization but does not prevent it at long times. We further demonstrate that the inclusion of effective non-Hermitian spin relaxation processes can substantially stabilize the GZ states, leading to a nonequilibrium steady state with finite fidelity with GZ state. Such dissipative processes can naturally originate from mechanisms such as Purcell-enhanced spontaneous emission or spin-lattice relaxation in the presence of the helical magnetic field. Using infinite time-evolving block decimation and exact time evolution, we systematically analyze the dynamics and robustness of the GZ states in the perturbed non-Hermitian XYZ model. To connect with experimental platforms, we introduce a Hubbard model that maps onto the XYZ spin system and propose that ring-shaped optical lattices may provide a viable route for realizing and stabilizing GZ states. Finally, we present an equivalent Lindblad description of the effective non-Hermitian dynamics.

Related papers

• Evidence for a two-dimensional quantum glass state at high temperatures [108.88989889650607]
  Disorder in quantum many-body systems can drive transitions between ergodic and non-ergodic phases.<n>We study an interacting spin model at finite temperature in a disordered landscape.<n>Our results show that there is a transition out of the ergodic phase in two-dimensional systems.
  arXiv  Detail & Related papers  (2026-01-04T00:09:50Z)
• Frequency-resolved Purcell effect for the dissipative generation of steady-state entanglement [49.1574468325115]
  We report a driven-dissipative mechanism to generate stationary entangled $W$ states among strongly-interacting quantum emitters placed within a cavity. The non-harmonic energy structure of the interacting ensemble allows this transition to be resonantly selected by the cavity. Evidence of this purely dissipative mechanism should be observable in state-of-the-art cavity QED systems in the solid-state.
  arXiv  Detail & Related papers  (2023-12-19T18:04:22Z)
• Stable dynamic helix state in the nonintegrable XXZ Heisenberg model [3.6107264108886996]
  We investigate the influence of external fields on the stability of spin helix states in an XXZ Heisenberg model. As long as the system remains chaotic, the scar extent of the helix state shows no significant variation.
  arXiv  Detail & Related papers  (2023-08-11T14:14:40Z)
• Fixed lines in a non-Hermitian Kitaev chain with spatially balanced pairing processes [0.0]
  Exact solutions for non-Hermitian quantum many-body systems are rare but may provide valuable insights into the interplay between Hermitian and non-Hermitian components. We report our investigation of a non-Hermitian variant of a p-wave Kitaev chain by introducing staggered imbalanced pair creation and quench terms.
  arXiv  Detail & Related papers  (2023-04-30T14:41:42Z)
• Quantum Metrology Protected by Hilbert Space Fragmentation [0.0]
  coherent quantum dynamics employing the Hilbert-space fragmentation (HSF) We show that the emergent HSF caused by strong Ising interactions enables us to design a stable state where part of the spins is effectively decoupled from the rest of the system. Using the decoupled spins as a probe to measure a transverse field, we demonstrate that the Heisenberg limited sensitivity is achieved without suffering from thermalization.
  arXiv  Detail & Related papers  (2022-11-17T14:51:22Z)
• Sufficient condition for gapless spin-boson Lindbladians, and its connection to dissipative time-crystals [64.76138964691705]
  We discuss a sufficient condition for gapless excitations in the Lindbladian master equation for collective spin-boson systems. We argue that gapless modes can lead to persistent dynamics in the spin observables with the possible formation of dissipative time-crystals.
  arXiv  Detail & Related papers  (2022-09-26T18:34:59Z)
• Steady helix states in a resonant XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction [0.0]
  We show that a set of precession helix states can be constructed by deliberate superposition of degenerate eigenstates of the Hamiltonian under the resonant condition. When a non-Hermitian balance boundary term is imposed as a quenching action, a steady helix state emerges from some easily prepared initial states.
  arXiv  Detail & Related papers  (2022-09-09T03:23:02Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Analog cosmological reheating in an ultracold Bose gas [58.720142291102135]
  We quantum-simulate the reheating-like dynamics of a generic cosmological single-field model in an ultracold Bose gas. Expanding spacetime as well as the background oscillating inflaton field are mimicked in the non-relativistic limit. The proposed experiment has the potential of exploring the evolution up to late times even beyond the weak coupling regime.
  arXiv  Detail & Related papers  (2020-08-05T18:00:26Z)
• Non-equilibrium non-Markovian steady-states in open quantum many-body systems: Persistent oscillations in Heisenberg quantum spin chains [68.8204255655161]
  We investigate the effect of a non-Markovian, structured reservoir on an open Heisenberg spin chain. We establish a coherent self-feedback mechanism as the reservoir couples frequency-dependent to the spin chain.
  arXiv  Detail & Related papers  (2020-06-05T09:16:28Z)
• Deconstructing effective non-Hermitian dynamics in quadratic bosonic Hamiltonians [0.0]
  We show that stability-to-instability transitions may be classified in terms of a suitably generalized $mathcalPmathcalT$ symmetry. We characterize the stability phase diagram of a bosonic analogue to the Kitaev-Majorana chain under a wide class of boundary conditions. Our analysis also reveals that boundary conditions that support Majorana zero modes in the fermionic Kitaev chain are precisely the same that support stability in the bosonic chain.
  arXiv  Detail & Related papers  (2020-03-06T19:30:51Z)

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.