Probing Tensor Singularities and Their Euler-Class Descendants via Non-Abelian Quantum Geometry Measurement

• URL: http://arxiv.org/abs/2605.17977v1
• Date: Mon, 18 May 2026 07:30:57 GMT
• Title: Probing Tensor Singularities and Their Euler-Class Descendants via Non-Abelian Quantum Geometry Measurement
• Abstract summary: We predict and observe a new class of four-dimensional (4D) tensor singularities and their three-dimensional (3D) Euler-class descendants on a superconducting circuit platform.<n>Our work establishes a robust experimental framework for exploring high-order gauge theory and real-bundle topology across diverse quantum platforms.
• Score: 4.371585619583345
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We report the theoretical prediction and experimental observation of a new class of four-dimensional (4D) tensor singularities and their three-dimensional (3D) Euler-class descendants, protected by chiral and spacetime inversion symmetries on a superconducting circuit platform. The 4D point-like singularity/monopole, characterized by the Dixmier-Douady class of a real bundle gerbe associated with tensor gauge fields, is observed to evolve into a nodal ring carrying an additional first Euler class charge under symmetry-preserving perturbations. Dimensional reduction reveals 3D Euler and Euler curvature dipoles, exhibiting nontrivial Euler topology and a topological sum rule that ensures zero-energy flat bands inherit nontrivial topology even without interactions. Crucially, these high-dimensional degenerate systems are mapped and reconstructed using a hybrid analog-digital protocol designed for non-Abelian quantum geometry measurement within a superconducting qubit array. Our work not only expands the family of topological monopoles but also establishes a robust experimental framework for exploring high-order gauge theory and real-bundle topology across diverse quantum platforms.

Related papers

• Unitary discretization of the Koopman-von Neumann equation for quantum simulation of fluid and plasma dynamics [45.88028371034407]
  KvN framework embeds the Liouville equation into a Hilbert space with norm-preserving, unitary evolution.<n>Weyl-ordered KvN generator is derived as the unique anti-Hermitian operator symmetrization for real velocity fields.
  arXiv  Detail & Related papers  (2026-05-18T23:27:02Z)
• Dual Quantum Geometric Tensors and Local Topological Invariant [1.8205293871050265]
  We show that the Zeeman QGT is generically non-Hermitian and admits a natural decomposition into normal and anomalous metric-curvature sectors.<n>The results establish a unified framework connecting non-Hermitian Zeeman quantum geometry, local Dirac-node topology, and measurable transport signatures.
  arXiv  Detail & Related papers  (2026-04-09T08:00:50Z)
• Extending Topological Bound on Quantum Weight Beyond Symmetry-Protected Topological Phases [0.8070255453341216]
  We show that topological invariants defined via the projected spectrum lower-bound the quantum weight with a symmetry-breaking correction to the quantum metric.<n>Our proposed bound holds even when the underlying symmetries are broken, and it would be amenable to experimental verification via the optical conductivity sum rule.
  arXiv  Detail & Related papers  (2026-03-13T14:49:25Z)
• 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)
• Nonequilibrium Probes of Quantum Geometry in Gapless Systems [0.0]
  Much of our understanding of gapless many-body quantum systems stems from their low-energy descriptions as conformal field theories.<n>This is especially true in 1+1 dimensions, where such theories have an infinite-dimensional parameter space induced by their conformal symmetry.<n>We reveal the associated quantum geometry by considering finite systems driven by time-dependent conformal transformations.
  arXiv  Detail & Related papers  (2025-11-12T19:00:05Z)
• Engineering of Anyons on M5-Probes via Flux Quantization [0.0]
  We develop a novel derivation of anyonic topological order on single magnetized M5-branes.<n>The rigorous construction is non-Lagrangian and non-perturbative.<n>Results imply from this the quantum observables and modular functor of abelian Chern-Simons theory.
  arXiv  Detail & Related papers  (2025-01-29T19:00:04Z)
• Quantum geometric bounds in spinful systems with trivial band topology [0.0]
  We derive quantum geometric bounds in spinful systems characterized by a single $mathbbZ$ index protected by a spin gap.<n>Our bounds provide geometric conditions on the spin topology, distinct from the known quantum geometric bounds associated with Wilson loops and nontrivial band topologies.<n>We benchmark these findings with first-principles calculations in elemental bismuth realizing a nontrivial even spin-Chern number.
  arXiv  Detail & Related papers  (2025-01-27T19:00:02Z)
• Gauge-invariant projector calculus for quantum state geometry and applications to observables in crystals [44.99833362998488]
  More complex aspects of geometry emerge in properties linking multiple bands, such as optical responses.<n>We identify novel multi-state geometrical invariants using an explicitly gauge-invariant formalism based on projection operators.<n>We provide more detail on the projector formalism and the geometrical invariants arising in the vicinity of a specific value of crystal momentum.
  arXiv  Detail & Related papers  (2024-12-04T19:00:00Z)
• The multi-state geometry of shift current and polarization [44.99833362998488]
  We employ quantum state projectors to develop an explicitly gauge-invariant formalism.<n>We provide a simple expression for the shift current that resolves its precise relation to the moments of electronic polarization.<n>We demonstrate its power with applications to non-linear optics and the theory of electronic polarization.
  arXiv  Detail & Related papers  (2024-09-24T18:00:02Z)
• Non-Gaussian superradiant transition via three-body ultrastrong coupling [62.997667081978825]
  We introduce a class of quantum optical Hamiltonian characterized by three-body couplings. We propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model.
  arXiv  Detail & Related papers  (2022-04-07T15:39:21Z)
• Probing chiral edge dynamics and bulk topology of a synthetic Hall system [52.77024349608834]
  Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. Here, we realize a quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension. We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviors.
  arXiv  Detail & Related papers  (2020-01-06T16:59:08Z)

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.