A new approach to the Kondo effect: sophomore's dream function and Lee-Yang zeros
Abstract
We develop an analytical approach to the Kondo problem based on an effective partition function that generalizes the sophomore's dream integral. The Kondo crossover is represented as a passage through an approximately equidistant ladder of its Lee-Yang zeros in the complex plane, rather than as a singularity on the real axis. Summation over this ladder yields the Gamma function Γ(α+ TK/(2 πT)) as the universal crossover backbone, where the offset α=1/2 is fixed by the Friedel sum rule. The Euler-Maclaurin expansion connects the discrete zero structure to the Nozieres Fermi-liquid theory through Bernoulli numbers. A two-cutoff formula provides a compact, essentially one-parameter description of the full crossover in terms of a temperature-space Fano lineshape which is a thermal average of the energy-space Fano resonance observed in STM. Drift corrections are treated. The approach extends to SU(N) Coqblin-Schrieffer, underscreened and Anderson impurity models, and Kondo lattices.
Versions
Related
- Lee-Yang zeros and edge singularity in a mean-field approach
- Lee-Yang zeros of modulated XY spin chains with Dzyaloshinskii-Moriya interaction: zero-contour topology and quantum phase-diagram reconstruction
- Green-function Zeros Encode Competing Mott and Charge-ordering Scales
- Four-loop beta function in N=2 supersymmetric Yang-Mills theory, dimensional reduction, and treatment of γ5
- Localization transition in a charge-Kondo circuit
BibTeX
@misc{irkhin2026approach,
title = {{A new approach to the Kondo effect: sophomore's dream function and Lee-Yang zeros}},
author = {V. Yu. Irkhin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13666},
eprint = {2610.13666},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13666},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A new approach to the Kondo effect: sophomore's dream function and Lee-Yang zeros
AU - V. Yu. Irkhin
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13666
UR - https://arxiv.org/abs/2610.13666
AB - We develop an analytical approach to the Kondo problem based on an effective partition function that generalizes the sophomore's dream integral. The Kondo crossover is represented as a passage through an approximately equidistant ladder of its Lee-Yang zeros in the complex plane, rather than as a singularity on the real axis. Summation over this ladder yields the Gamma function Γ(α+ T_K/(2 πT)) as the universal crossover backbone, where the offset α=1/2 is fixed by the Friedel sum rule. The Euler-Maclaurin expansion connects the discrete zero structure to the Nozieres Fermi-liquid theory through Bernoulli numbers. A two-cutoff formula provides a compact, essentially one-parameter description of the full crossover in terms of a temperature-space Fano lineshape which is a thermal average of the energy-space Fano resonance observed in STM. Drift corrections are treated. The approach extends to SU(N) Coqblin-Schrieffer, underscreened and Anderson impurity models, and Kondo lattices.
ER -