Berry-Landau Fermi-liquid theory: transport in presence of quantum geometry
Abstract
Landau Fermi-liquid theory characterizes interacting metals through quasiparticles and their residual interactions. It is a challenge to incorporate non-trivial quantum geometry -- as encoded by Berry phases and the quantum metric -- as a fundamental ingredient. We formulate a Berry-Landau Fermi-liquid theory for spinless fermions within an isolated band crossing the Fermi surface and derive the Landau functional through the Nozières--Luttinger construction. The instantaneous response to a perturbation of the Bloch waves generates both an anomalous Berry-connection potential in the action and an interaction-induced quantum-geometric contribution to the quasiparticle current. The conserved physical charge current is then obtained via the electromagnetic Ward identity as a combinati of this quantum-geometric current and the bare drift current. Therefore, the intrinsic anomalous Hall conductivity is fixed by the Berry-curvature integral of the dressed quasiparticle band while the Drude weight contains both conventional and quantum-geometric contributions. In the presence of Galilean symmetry, the Drude weight is protected against interaction renormalization. In the flat/narrow-band limit, transport is dominantly quantum-geometric and can be thermally enhanced. These results establish quasiparticle occupations, Landau interactions, and the quantum geometry carried by quasiparticles as the fundamental low-energy ingredients of a Berry-Landau Fermi liquid.
Related
- Scaling analysis of quantum geometry in second-order nonlinear transport
- Quantum fluctuation-driven transport crossover between two liquid states in distinguishable helium-4
- The Geometry of Transport in Quantum Walks and Parrondo's Paradox
- Landau theory applied to antiferroelectric ordering in ferroelectric nematic liquid crystals
- Modular Landau Analysis of Coupled Phase Transitions: Application to Ferroelectric Liquid Crystals
BibTeX
@misc{chen2026berrylandau,
title = {{Berry-Landau Fermi-liquid theory: transport in presence of quantum geometry}},
author = {Shuai A. Chen and Roderich Moessner},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26632},
eprint = {2609.26632},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26632},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Berry-Landau Fermi-liquid theory: transport in presence of quantum geometry
AU - Shuai A. Chen
AU - Roderich Moessner
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26632
UR - https://arxiv.org/abs/2609.26632
AB - Landau Fermi-liquid theory characterizes interacting metals through quasiparticles and their residual interactions. It is a challenge to incorporate non-trivial quantum geometry -- as encoded by Berry phases and the quantum metric -- as a fundamental ingredient. We formulate a Berry-Landau Fermi-liquid theory for spinless fermions within an isolated band crossing the Fermi surface and derive the Landau functional through the Nozières--Luttinger construction. The instantaneous response to a perturbation of the Bloch waves generates both an anomalous Berry-connection potential in the action and an interaction-induced quantum-geometric contribution to the quasiparticle current. The conserved physical charge current is then obtained via the electromagnetic Ward identity as a combinati of this quantum-geometric current and the bare drift current. Therefore, the intrinsic anomalous Hall conductivity is fixed by the Berry-curvature integral of the dressed quasiparticle band while the Drude weight contains both conventional and quantum-geometric contributions. In the presence of Galilean symmetry, the Drude weight is protected against interaction renormalization. In the flat/narrow-band limit, transport is dominantly quantum-geometric and can be thermally enhanced. These results establish quasiparticle occupations, Landau interactions, and the quantum geometry carried by quasiparticles as the fundamental low-energy ingredients of a Berry-Landau Fermi liquid.
ER -