Geometric Protection of Bipartite Entanglement in Hopf-Linked Quantum Rings

• URL: http://arxiv.org/abs/2605.26622v1
• Date: Tue, 26 May 2026 07:00:21 GMT
• Title: Geometric Protection of Bipartite Entanglement in Hopf-Linked Quantum Rings
• Abstract summary: We determine the bipartite entanglement bounds of two interacting electrons in deeply interlocked Hopf-linked quantum rings.<n>This identifies an exact continuous spatial symmetry that geometrically isolates the positive-parity Bell state.<n>Our analysis shows that the resulting bounding conditions reveal scaling limitations in mesoscopic semiconductor architectures.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We determine the bipartite entanglement bounds of two interacting electrons in deeply interlocked Hopf-linked quantum rings via exact diagonalization of the unexpanded 3D Coulomb interaction. This identifies an exact continuous spatial symmetry that geometrically isolates the positive-parity Bell state, preventing classical interaction-driven localization. A non-coplanar geometric tilt ($α> 0$) is essential to lift the exchange degeneracy and maintain this maximally entangled manifold as a state of frozen entanglement. However, a higher-order Schrieffer-Wolff transformation demonstrates this geometric protection is fundamentally bounded; uncancelled inter-orbital momentum transitions inevitably induce dynamical parity mixing. This defines a critical interaction threshold ($λ_{crit}$) for irreversible entanglement collapse. Our analysis shows that the resulting bounding conditions reveal scaling limitations in mesoscopic semiconductor architectures, dictating the necessity of synthetic macroscopic platforms to achieve robust topological protection.

Related papers

• Nonlocality-induced critical-length hierarchy from non-Hermitian competition [48.9823527611878]
  In short-range systems formed by two coupled chains, competition leads to the critical-length law $N_csimln D$.<n>Here we show that long-range hoppings fundamentally reorganizes this critical behavior, producing a hierarchy of distinct scaling laws.<n>Our results offer a platform-independent framework testable in programmable topoelectrical circuits, photonic lattices and digital quantum simulators.
  arXiv  Detail & Related papers  (2026-08-03T18:00:18Z)
• Magnetic long-range order at finite temperature in two-dimensional hyperbolic lattices [45.88028371034407]
  Infrared singularities of gapless Goldstone modes preclude magnetic long-range order at finite temperature in conventional two-dimensional systems.<n>We find that the zero-energy collective modes required by symmetry carry vanishing local spectral weight.<n>We estimate the ordering temperature from the thermal spin-wave correction to the ordered moment.
  arXiv  Detail & Related papers  (2026-06-25T18:00:01Z)
• Engineering Quantum Many-Body Scars through Lattice Geometry [0.0028001975341488856]
  We show that lattice geometry alone can serve as a powerful and experimentally accessible control for inducing and enhancing scarring.<n>By transforming a one-dimensional chain into a quasi-one-dimensional triangle-decorated lattice, we find that the fully polarized state exhibits pronounced fidelity revivals, slow entanglement growth, and strong overlap with a tower of weakly entangled eigenstates.
  arXiv  Detail & Related papers  (2026-05-06T18:00:01Z)
• Unconventional entanglement scaling and quantum criticality in the long-range spin-one Heisenberg chain with single-ion anisotropy [0.0]
  Long-range interactions can fundamentally reshape the low-energy properties of low-dimensional quantum matter.<n>We determine the ground-state phase diagram and critical properties of the spin-one Heisenberg chain with single-ion anisotropy and staggered antiferromagnetic power-law interactions.<n>Our work positions this model as a target for near-term atomic platforms with tunable long-range couplings and exhibiting natural single-ion anisotropy.
  arXiv  Detail & Related papers  (2026-04-14T14:01:37Z)
• Tunable information insulation induced by constraint mismatch [0.0]
  We study a composite model of two $1D$ $PXP$ chains with dual constraints.<n>Multiple frozen junctions shatter the Hilbert space into disjoint Krylov fragments.<n>Chirally protected zero-energy mode can exist which has local peaks at the physical edges and within the bulk near the junction sites.
  arXiv  Detail & Related papers  (2026-04-01T10:53:39Z)
• A two-dimensional realization of the parity anomaly [0.0]
  Quantum anomalies arise when symmetries of a classical theory cannot be preserved upon quantization.<n>A prominent example is the parity anomaly of a single two-dimensional Dirac fermion, which enforces a half-quantized Hall response.<n>We report the observation of a parity-anomalous Hall response at the critical point of a quantum Hall phase transition in a synthetic two-dimensional system of ultracold dysprosium atoms.
  arXiv  Detail & Related papers  (2026-03-23T16:34:45Z)
• Hysteretic squashed entanglement in many-body quantum systems [42.085941481155295]
  Entanglement in many-body quantum systems is distributed across spatial regions.<n>We propose hysteretic entanglement $T_sq$, a conditional entanglement that measures the genuine quantum correlations between two subregions.<n>We show that $T_sq$ can detect genuine quantum correlations across both adjacent and long-range subsystems.
  arXiv  Detail & Related papers  (2026-03-10T17:00:49Z)
• Symmetry-protected topology and deconfined solitons in a multi-link $\mathbb{Z}_2$ gauge theory [45.88028371034407]
  We study a $mathbbZ$ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell.<n>We show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability.<n>By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization.
  arXiv  Detail & Related papers  (2026-03-02T22:59:25Z)
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation [39.146761527401424]
  We explore the finite-density phase diagram of the single-flavour Gross-Neveu-Wilson (GNW) model.<n>We find a sequence of inhomogeneous ground states that arise through a real-space version of the mechanism of Hilbert-space fragmentation.
  arXiv  Detail & Related papers  (2025-06-23T14:19:35Z)
• Geometric Quantum Gates of Non-closed Paths Under Counterdiabatic Driving [7.02926424024021]
  Non-adiabatic and non-closed evolutionary paths play a significant role in the fidelity of quantum gates.<n>We propose a high-fidelity quantum control framework based on the quasi-topological number ($nu_textqua$)<n>We bridge geometric quantum control with topological protection, offering a universal approach to noise-resistant quantum computing.
  arXiv  Detail & Related papers  (2025-04-09T08:35:43Z)
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
  We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
  arXiv  Detail & Related papers  (2023-05-11T15:57:27Z)
• Tuning long-range fermion-mediated interactions in cold-atom quantum simulators [68.8204255655161]
  Engineering long-range interactions in cold-atom quantum simulators can lead to exotic quantum many-body behavior. Here, we propose several tuning knobs, accessible in current experimental platforms, that allow to further control the range and shape of the mediated interactions.
  arXiv  Detail & Related papers  (2022-03-31T13:32:12Z)
• 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)

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.