Categorical classification of non-Fermi liquids in 2+1 dimensions
Abstract
A defining feature of non-Fermi liquids is a lack of the quasiparticle peak on the Fermi surface in the spectral function, which is usually realized by coupling a finite density of fermions with critical collective fluctuations. However, these features of the two- and three-point vertex functions are qualitatively the same across many non-Fermi liquids, which has made it difficult to classify them beyond the definition by negation. We point out that the four-point function in the pairing channel contains rich information that positively differentiates distinct types of non-Fermi liquids. Using the generalized notion of fixed points that captures scale-dependent universal pairing interaction, we provide a non-perturbative classification of 2+1-dimensional non-Fermi liquids. In the large Fermi momentum limit with fixed dimensionless couplings, metals coupled with long-wavelength critical fluctuations are classified into seven superuniversality classes. Each of them exhibits a unique phase diagram in the space of temperature and bare four-fermion coupling. The present work generalizes the earlier perturbative classification to strongly interacting non-Fermi liquids by leveraging kinematic constraints.
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BibTeX
@misc{kukreja2026categorical,
title = {{Categorical classification of non-Fermi liquids in 2+1 dimensions}},
author = {Shubham Kukreja and Dawson M. Willerton and Sung-Sik Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25713},
eprint = {2610.25713},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25713},
}
RIS
TY - UNPB
TI - Categorical classification of non-Fermi liquids in 2+1 dimensions
AU - Shubham Kukreja
AU - Dawson M. Willerton
AU - Sung-Sik Lee
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25713
UR - https://arxiv.org/abs/2610.25713
AB - A defining feature of non-Fermi liquids is a lack of the quasiparticle peak on the Fermi surface in the spectral function, which is usually realized by coupling a finite density of fermions with critical collective fluctuations. However, these features of the two- and three-point vertex functions are qualitatively the same across many non-Fermi liquids, which has made it difficult to classify them beyond the definition by negation. We point out that the four-point function in the pairing channel contains rich information that positively differentiates distinct types of non-Fermi liquids. Using the generalized notion of fixed points that captures scale-dependent universal pairing interaction, we provide a non-perturbative classification of 2+1-dimensional non-Fermi liquids. In the large Fermi momentum limit with fixed dimensionless couplings, metals coupled with long-wavelength critical fluctuations are classified into seven superuniversality classes. Each of them exhibits a unique phase diagram in the space of temperature and bare four-fermion coupling. The present work generalizes the earlier perturbative classification to strongly interacting non-Fermi liquids by leveraging kinematic constraints.
ER -