Gradient flow towards quantum states with ideal quantum geometry

• URL: http://arxiv.org/abs/2608.19770v1
• Date: Thu, 20 Aug 2026 08:14:14 GMT
• Title: Gradient flow towards quantum states with ideal quantum geometry
• Abstract summary: gradient-flow method for quantum states in lattice models.<n>We show that due to a no-go theorem for finite-dimensional projectors, the two conditions cannot in general be satisfied simultaneously in lattice models.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a gradient-flow method for quantum states in lattice models, generated by an action consisting of the quantum-metric and the square of the Berry curvature. These two terms drive the spectral projector toward Bogomolny saturation and uniform Berry curvature, respectively. We show that, due to a no-go theorem for finite-dimensional projectors, the two conditions cannot in general be satisfied simultaneously in lattice models. Hence the flow is expected to approach a nontrivial fixed point that balances the two geometric requirements. For the Wilson-Dirac model, we demonstrate that the flowed projector exhibits almost uniform Berry curvature while remaining close to the Bogomolny bound. We further construct a short-range truncated flattened Hamiltonian from the flowed projector and obtain a lattice model with nearly flat bands and nearly uniform Berry curvature. We also apply the method to the Hofstadter model and confirm the roles of the metric and Berry-curvature terms in a Chern band with higher Chern number.

Related papers

• Exact analytical spectrum, eigenstates, and quantum geometry of the quarter-flux Harper-Hofstadter model [0.0]
  Quantum geometry has emerged as a guiding principle across atomic and condensed-matter physics.<n>We provide closed-form expressions for both the spectrum and the quantum geometry of a paradigmatic four-band model.<n>We evaluate fractional-Chern-insulator stability criteria analytically and quantify the lowest band of the quarter-flux Harper-Hofstadter model to be a nearly ideal Chern band.
  arXiv  Detail & Related papers  (2026-08-26T17:58:52Z)
• Quantum model for black holes and clocks [41.99844472131922]
  We consider a stationary quantum system consisting of two non-interacting yet entangled subsystems, $$ and $$.<n>We identify a quantum theory characterizing $$ such that, in the quantum-to-classical crossover of the composite system, $$ behaves as a test particle within the gravitational field of a Schwarzschild Black Hole.<n>This leads us to discuss how the quantum model for $$ endows the SBH with all the characteristics of a "perfect" clock.
  arXiv  Detail & Related papers  (2026-01-12T11:26:06Z)
• A Gauss-Bonnet Theorem for Quantum States: Gauss Curvature and Topology in the Projective Hilbert Space [0.0]
  We calculate the curvature of the quantum metric of Bloch bands using a gauge-invariant formulation based on eigenprojectors.<n>We find that the Gauss curvature is constant over regular regions, but the manifold inevitably develops a closed curve of singular points.<n>By introducing the notion of a front and a signed area form, we derive a generalized Gauss-Bonnet relation that includes a singular curvature term defined along the fold curve.
  arXiv  Detail & Related papers  (2025-10-17T15:50:03Z)
• Non-Hermitian Realization of Quantum Dynamics on Embedded Manifolds [0.0]
  We show that the Floquet Hamiltonian of a quantum particle driven by a general time-periodic imaginary potential is exactly equivalent at stroboscopic times.<n>We illustrate the construction for a sinusoidal drive and for the torus of revolution, and outline how the framework can guide experimental design of curved-space quantum dynamics.
  arXiv  Detail & Related papers  (2025-10-13T18:55:16Z)
• 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)
• Bayesian Circular Regression with von Mises Quasi-Processes [57.88921637944379]
  In this work we explore a family of expressive and interpretable distributions over circle-valued random functions.<n>For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Gibbs sampling.<n>We present experiments applying this model to the prediction of wind directions and the percentage of the running gait cycle as a function of joint angles.
  arXiv  Detail & Related papers  (2024-06-19T01:57:21Z)
• Emergent Spacetime in Quantum Lattice Models [0.0]
  Many quantum lattice models have an emergent relativistic description in their continuum limit. In this thesis, we investigate novel features of this relativistic description for a range of quantum lattice models. We show how to generate emergent curved spacetimes and identify observables at the lattice level which reveal this emergent behaviour.
  arXiv  Detail & Related papers  (2022-12-23T19:00:04Z)
• Penrose dodecahedron, Witting configuration and quantum entanglement [55.2480439325792]
  A model with two entangled spin-3/2 particles based on geometry of dodecahedron was suggested by Roger Penrose. The model was later reformulated using so-called Witting configuration with 40 rays in 4D Hilbert space. Two entangled systems with quantum states described by Witting configurations are discussed in presented work.
  arXiv  Detail & Related papers  (2022-08-29T14:46:44Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness [68.8204255655161]
  We compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models. In the dissipative model, the non-unitary effects arise from the outflow of photons through the cavity walls. We show the geometric phase is robust, exhibiting a vanishing correction under a non-unitary evolution.
  arXiv  Detail & Related papers  (2021-10-27T15:27:54Z)
• Chern number and Berry curvature for Gaussian mixed states of fermions [0.0]
  We generalize the concept of topological invariants for mixed states based on the ensemble geometric phase. The Chern number can be expressed as an integral of the Berry curvature of the so-called fictitious Hamiltonian.
  arXiv  Detail & Related papers  (2021-04-25T09:39:32Z)
• Perils of Embedding for Quantum Sampling [0.0]
  A common approach is to minor embed the desired Hamiltonian in a native Hamiltonian. Here, we consider quantum thermal sampling in the transverse-field Ising model. We simulate systems of much larger sizes and larger transverse-field strengths than would otherwise be possible.
  arXiv  Detail & Related papers  (2021-03-12T01:49:52Z)

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.