Quantum Geometry Phenomena in Condensed Matter Systems
cond-mat.str-el
Submitted: 2025-08-01
Updated: 2025-08-01
Comments: Your comments and suggestions are welcome! (62 pages, 28 figures)
Journal ref: Rev. Mod. Phys. 98, 035005 (2026)
DOI: 10.1103/f78t-ky69
License: http://creativecommons.org/publicdomain/zero/1.0/
The gist: Quantum geometry, which describes the geometry of Bloch wavefunctions in solids, has become a cornerstone of modern quantum condensed matter physics.
Terminology
Abstract
Quantum geometry, which describes the geometry of Bloch wavefunctions in solids, has become a cornerstone of modern quantum condensed matter physics. The quantum geometrical tensor encodes this geometry through two fundamental components: the quantum metric (real part) and the Berry curvature (imaginary part). While the Berry curvature gained prominence through its manifestation in the intrinsic anomalous Hall effect, recent advances have revealed equally significant effects arising from the quantum metric. This includes its signatures in nonlinear transport, superfluid density of flat-band superconductors, and nonlinear optical responses. These advances underscore how quantum geometry is reshaping our understanding of condensed matter systems, with far-reaching implications for future technologies. In this review, we survey recent progress in the field, focusing on both foundational concepts and emergent phenomena in transport and optics-with particular emphasis on the pivotal role of the quantum metric.
Sources
- The multi-state geometry of shift current and polarization
- Phonon thermal Hall as a lattice Aharonov-Bohm effect
- Probing the Quantum Geometry of Correlated Metals using Optical Conductivity
- The Effect of the Non-Abelian Quantum Metric on Superfluidity
- Quantum Metric Nonlinear Spin-Orbit Torque Enhanced by Topological Bands
- Scaling analysis of quantum geometry in second-order nonlinear transport
- Mixed axial-gravitational anomaly from emergent curved spacetime in nonlinear charge transport
- Scaling Law for Time-Reversal-Odd Nonlinear Transport
- Revealing Quantum Geometry in Nonlinear Quantum Materials
- Quantum geometric bound for saturated ferromagnetism
- Quantum geometric ferromagnetism by singular saddle point
- Orbital magnetoelectric coupling of three dimensional Chern insulators
- Experimental measurement of the divergent quantum metric of an exceptional point
- Gauge-invariant projector calculus for quantum state geometry and applications to observables in crystals
- Supercell Wannier Functions and Emergent Kondo Lattices in Topological Bands
- Evidence of Momentum Space Condensation in Rhombohedral Hexalayer Graphene
- Quantum weight
- Fractional Quantum Hall Physics in Topological Flat Bands
- Witnessing Quantum Entanglement Using Resonant Inelastic X-ray Scattering
- Geometrical meaning of the Drude weight and its relationship to orbital magnetization
Related papers
- Microscopic Constructions of the BF+AAB Topological Field Theory and Borromean-Rings Braiding in (3+1) Dimensions
- Transport in the emergent Bose liquid: Bad metal, strange metal, and weak insulator, all in one system
- Gibbs-state phases beyond microscopic symmetry breaking: A phase invariant for the 3D toric code
- Instabilities in self-consistent diagrammatic approaches and how to cure them
- True vs false Fermi surfaces in the Pseudogap regime and their transformation with doping and temperature in the Hubbard Model
- Orbital magnetic susceptibility and de Haas-van Alphen effect of a flat band from quantum geometry