Geometric Ginzburg-Landau theory of charge ordering and commensurability
Abstract
The concept of quantum geometry has recently led to reinvigorated insights in a wide range of fields including physical responses, superconductivity, and optical transitions, with effects most pronounced in systems with nearly flat dispersion. Here, we show that it plays an essential role in charge density wave formation (CDW) -- an important physical phenomenon that is responsible for driving various sharp changes in material transport properties including metal-insulator transitions. We derive an effective Ginzburg-Landau theory including uncharted contributions and, as a highlight, discover a general criterion for both CDW formation and commensurability transitions where underlying electron-phonon interactions manifest purely as electronic quantum geometric enhancements/suppressions. We benchmark our framework in a class of transition-metal dichalcogenides and resolve a longstanding puzzle where well-established purely kinetic CDW criteria fail in describing the correct ordering wavevector. Besides rendering robust criteria and fundamental insights that are immediately relevant to several experimental charge ordering systems, our theory can also be applied directly to other phonon-mediated phases such as superconductivity, and can be used as an important tool to explore the interplay between various such states. More generally, our framework provides a recipe for investigating the role of quantum geometry in phase transitions.
Related
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BibTeX
@misc{agarwal2026geometric,
title = {{Geometric Ginzburg-Landau theory of charge ordering and commensurability}},
author = {Aneesh Agarwal and Rutvij Gholap and Mohammad Saeed Bahramy and Robert-Jan Slager},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10678},
eprint = {2609.10678},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10678},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geometric Ginzburg-Landau theory of charge ordering and commensurability
AU - Aneesh Agarwal
AU - Rutvij Gholap
AU - Mohammad Saeed Bahramy
AU - Robert-Jan Slager
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10678
UR - https://arxiv.org/abs/2609.10678
AB - The concept of quantum geometry has recently led to reinvigorated insights in a wide range of fields including physical responses, superconductivity, and optical transitions, with effects most pronounced in systems with nearly flat dispersion. Here, we show that it plays an essential role in charge density wave formation (CDW) -- an important physical phenomenon that is responsible for driving various sharp changes in material transport properties including metal-insulator transitions. We derive an effective Ginzburg-Landau theory including uncharted contributions and, as a highlight, discover a general criterion for both CDW formation and commensurability transitions where underlying electron-phonon interactions manifest purely as electronic quantum geometric enhancements/suppressions. We benchmark our framework in a class of transition-metal dichalcogenides and resolve a longstanding puzzle where well-established purely kinetic CDW criteria fail in describing the correct ordering wavevector. Besides rendering robust criteria and fundamental insights that are immediately relevant to several experimental charge ordering systems, our theory can also be applied directly to other phonon-mediated phases such as superconductivity, and can be used as an important tool to explore the interplay between various such states. More generally, our framework provides a recipe for investigating the role of quantum geometry in phase transitions.
ER -