Quantum Geometric Tensor in the Wild: Resolving Stokes Phenomena via Floquet-Monodromy Spectroscopy

• URL: http://arxiv.org/abs/2512.20253v1
• Date: Tue, 23 Dec 2025 11:12:03 GMT
• Title: Quantum Geometric Tensor in the Wild: Resolving Stokes Phenomena via Floquet-Monodromy Spectroscopy
• Abstract summary: "Stokes Invariant" serves as the next-generation quantum number for classifying phases of matter beyond the reach of conventional topology.<n>We experimentally extract the hidden textitStokes Phenomenon -- the "missing" geometric data that completes the topological description.<n>We validate this framework on a superconducting qudit model, demonstrating that the "Stokes Invariant" serves as the next-generation quantum number.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Standard topological invariants, such as the Chern number and Berry phase, form the bedrock of modern quantum matter classification. However, we demonstrate that this framework undergoes a \textbf{catastrophic failure} in the presence of essential singularities -- ubiquitous in open, driven, and non-Hermitian systems ("Wild" regime). In these settings, the local geometric tensor diverges, rendering standard invariants ill-defined and causing perturbative predictions to deviate from reality by order unity ($\sim 100\%$). We resolve this crisis by introducing the \textbf{Floquet-Monodromy Spectroscopy (FMS)} protocol, a pulse-level control sequence, which experimentally extracts the hidden \textit{Stokes Phenomenon} -- the "missing" geometric data that completes the topological description. By mapping the singularity's Stokes multipliers to time-domain observables, FMS provides a rigorous experimental bridge to \textbf{Resurgence Theory}, allowing for the exact reconstruction of non-perturbative physics from divergent asymptotic series. We validate this framework on a superconducting qudit model, demonstrating that the "Stokes Invariant" serves as the next-generation quantum number for classifying phases of matter beyond the reach of conventional topology.

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)
• Anomalous Mixed-State Floquet Topology in One-Dimensional Open Quantum Systems [41.99844472131922]
  We investigate the non-equilibrium topology of a periodically driven, dissipative Su-Schrieffer-Heeger chain.<n>We show that the steady state can be characterised by a Hermitian purity spectrum.<n>We identify a pair of topological invariants $(0_mathrmEGP, _mathrmEGP)$, revealing a structure consistent with a $mathbbZtimesmathbbZ$ classification known from isolated Floquet SSH systems.
  arXiv  Detail & Related papers  (2026-04-28T05:54:40Z)
• Curvature-induced bound states in quantum wires [0.0]
  A classical particle under spatial constraints is strictly confined to live on a specific space manifold or path.<n>For particles constrained to different spaces, a formalism beyond the confinement potential approach is needed.<n>For a subclass fulfilling the additional requirement that the geometric potential is a distribution of first order, a solution scheme is presented.
  arXiv  Detail & Related papers  (2026-04-02T10:11:13Z)
• 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)
• 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)
• Twisted (co)homology of non-orientable Weyl semimetals [0.0]
  quasi-particle excitations in Weyl semimetals emerge in charge-conjugate pairs by the Nielsen-Ninomiya theorem.<n>When the Brillouin zone is non-orientable, this constraint is replaced by a $mathbbZ$ charge cancellation.
  arXiv  Detail & Related papers  (2025-11-27T10:31:56Z)
• Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits [0.0]
  Periodically driven systems intertwined with non-Hermiticity opens a rich arena for topological phases that transcend conventional Hermitian limits.<n>We analytically derive an effective Floquet Hamiltonian and formulate the generalized Brillouin zone for a periodically driven quasi-one-dimensional system.<n>Our study demonstrates that the skin effect remains robust across a broad range of driving parameters, and is notably amplified in the low-frequency regime.
  arXiv  Detail & Related papers  (2025-07-31T17:31:02Z)
• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• 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)
• Emergence of cosmic structure from Planckian discreteness [47.03992469282679]
  In the standard paradigm the inhomogeneities observed in the CMB arise from quantum fluctuations of an initially homogeneous and isotropic vacuum state.<n>We propose an alternative paradigm in which such inhomogeneities are present from the very beginning.<n>Specifically, inhomogeneities in the quantum state at the Planck scale propagate into semiclassical inhomogeneities on CMB scales.
  arXiv  Detail & Related papers  (2025-06-18T12:33:31Z)
• Avoided-crossings, degeneracies and Berry phases in the spectrum of quantum noise through analytic Bloch-Messiah decomposition [49.1574468325115]
  "analytic Bloch-Messiah decomposition" provides approach for characterizing dynamics of quantum optical systems.<n>We show that avoided crossings arise naturally when a single parameter is varied, leading to hypersensitivity of the singular vectors.<n>We highlight the possibility of programming the spectral response of photonic systems through the deliberate design of avoided crossings.
  arXiv  Detail & Related papers  (2025-04-29T13:14:15Z)
• Non-Hermitian wave-packet dynamics and its realization within a non-Hermitian chiral cavity [0.0]
  We derive the semiclassical equations of motion for a wave-packet in a non-Hermitian topological system.<n>We show that the complex Berry curvature introduces both an anomalous velocity and an anomalous force into the semiclassical EOM.<n>We suggest a potential experimental realization of this complex Haldane model using a non-Hermitian optical chiral cavity.
  arXiv  Detail & Related papers  (2025-01-21T14:15:14Z)
• Gapless Floquet topology [40.2428948628001]
  We study the existence of topological edge zero- and pi-modes despite the lack of bulk gaps in the quasienergy spectrum. We numerically study the effect of interactions, which give a finite lifetime to the edge modes in the thermodynamic limit with the decay rate consistent with Fermi's Golden Rule.
  arXiv  Detail & Related papers  (2024-11-04T19:05:28Z)
• 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)
• Non-Hermitian topological quantum states in a reservoir-engineered transmon chain [0.0]
  We show that a non-Hermitian quantum phase can be realized in a reservoir-engineered transmon chain. We show that genuine quantum effects are observable in this system via robust and slowly decaying long-range quantum entanglement of the topological end modes.
  arXiv  Detail & Related papers  (2022-10-06T15:21:21Z)
• Tuning the Topological $\ heta$-Angle in Cold-Atom Quantum Simulators of Gauge Theories [3.4075669047370125]
  We show how a tunable topological $theta$-term can be added to a prototype theory with gauge symmetry. The model can be realized experimentally in a single-species Bose--Hubbard model in an optical superlattice with three different spatial periods. This work opens the door towards studying the rich physics of topological gauge-theory terms in large-scale cold-atom quantum simulators.
  arXiv  Detail & Related papers  (2022-04-13T18:00:01Z)
• Topological fracton quantum phase transitions by tuning exact tensor network states [1.0753191494611891]
  Gapped fracton phases of matter generalize the concept of topological order. We employ an exact 3D quantum tensor-network approach to study a prototypical X cube fracton model.
  arXiv  Detail & Related papers  (2022-02-28T19:00:01Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems [0.0]
  We extend the nonequilibrium bosonic Dynamical Mean Field Theory to Markovian open quantum systems. As a first application, we address the steady-state of a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump.
  arXiv  Detail & Related papers  (2020-08-06T10:35:26Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)

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.