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Related Experiment Video

Updated: May 10, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

On the Kohn-Luttinger conundrum.

So Hirata¹, Xiao He

¹Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA. sohirata@illinois.edu

The Journal of Chemical Physics

|June 8, 2013

Summary

This summary is machine-generated.

A new renormalized many-body perturbation theory corrects the zero-temperature limit inconsistency in metals. This approach properly accounts for temperature effects in energies, resolving the Kohn-Luttinger conundrum for accurate many-body calculations.

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Area of Science:

Condensed Matter Physics
Quantum Many-Body Theory
Theoretical Chemistry

Background:

Conventional finite-temperature many-body perturbation theory exhibits an incorrect zero-temperature limit in metals, as identified by Kohn and Luttinger.
This inconsistency stems from neglecting temperature effects in the zeroth-order eigenstate energies.
This leads to the Kohn-Luttinger conundrum and differing correlation energy divergence rates in homogeneous electron gas (HEG) models.

Purpose of the Study:

To identify the source of the inconsistency in conventional finite-temperature many-body perturbation theory.
To propose a corrected theoretical framework that resolves the identified issues.
To ensure the theory's validity at both finite and zero temperatures.

Main Methods:

Analysis of the Kohn-Luttinger conundrum and its relation to temperature effects in perturbation theory.
Development of a renormalized many-body perturbation theory.
Application of finite-temperature extension of normal-ordered second quantization to energy denominators and numerators.

Main Results:

The proposed renormalized theory correctly reproduces the zero-temperature limit.
It resolves the inconsistency in correlation energy divergence rates observed in homogeneous electron gas (HEG) calculations.
The renormalized theory aligns with the established zero-temperature many-body perturbation theory.

Conclusions:

The noninclusion of temperature effects in zeroth-order eigenstate energies is the cause of the Kohn-Luttinger conundrum.
The developed renormalized many-body perturbation theory provides a consistent and accurate framework for finite-temperature calculations.
This work establishes the correct finite-temperature many-body perturbation theory for condensed matter systems.