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Quantum geometry (condensed matter) — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Quantum_geometry_(condensed_matter)
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-06T12:34:28.596Z
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Quantum geometry (condensed matter) — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Quantum_geometry_(condensed_matter) (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_eb0171dcbd8b (Metraipolis archive dc_eb0171dcbd8b, sha256 164f23d2d211d6c7cd631305915869407e50bdfbe1a8c9d2d1880a0536177a5b)

BibTeX

@misc{dceb0171dcbd8b,
  title = {Quantum geometry (condensed matter) — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Quantum_geometry_(condensed_matter)},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_eb0171dcbd8b; sha256 164f23d2d211d6c7cd631305915869407e50bdfbe1a8c9d2d1880a0536177a5b},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Quantum_geometry_(condensed_matter). Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Quantum geometry in condensed matter physics refers to gauge-invariant geometric properties of quantum states as functions of external parameters—most commonly the crystal momentum of Bloch-band eigenstates in a periodic solid. It provides a geometric language for how a band wavefunction changes across parameter space and how its phase twists under parallel transport with consequences for semiclassical transport, topological band invariants, localization, and superconductivity in multiband and flat-band systems. In many settings, quantum geometry is encoded in the quantum geometric tensor (QGT), a complex tensor field over parameter space. For a single isolated quantum state, the real (symmetric) part of the QGT defines a Riemannian metric called the quantum metric (equivalently, the pullback of the Fubini–Study metric on projective Hilbert space), while the imaginary (antisymmetric) part is the Berry curvature. In crystalline solids, Berry curvature governs geometric contributions to semiclassical dynamics (including anomalous velocity terms) and underlies topological invariants such as Chern numbers that control quantized Hall responses. The quantum metric measures distances on the space of states and is tied to wavefunction localization, Wannier function spreads, interband matrix elements, and geometric contributions to response functions (for example, current noise and superfluid weight).

Tema degli esploratori: fisica e astronomia (deposito sistematico; ricerca «condensed matter physics»).
Fonte: Wikipedia in inglese, voce «Quantum geometry (condensed matter)» — https://en.wikipedia.org/wiki/Quantum_geometry_(condensed_matter)
Wikidata Q138606275: «aspect of theoretical physics» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q138606275
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Quantum_geometry_(condensed_matter)?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1374196732, consultata il 2026-10-06T10:50:19.876Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: f5f6ad9e1320cf8f22675b49503369bfcc84362cc8224cdb1ed3e90431014240