Wilson chains are not thermal reservoirs

TL;DR

Wilson chains, used as models for quantum baths, cannot function as true thermal reservoirs because their temperature changes significantly with small energy additions, limiting their use in non-equilibrium long-time predictions.

Contribution

This paper demonstrates that Wilson chains are not suitable as thermal reservoirs due to their non-thermal response to energy input, impacting non-equilibrium studies.

Findings

Wilson chains' temperature shifts by order Delta E upon energy addition

They cannot reliably model thermal reservoirs in non-equilibrium scenarios

Implications for long-time behavior predictions in quantum impurity models

Abstract

Wilson chains, based on a logarithmic discretization of a continuous spectrum, are widely used to model an electronic (or bosonic) bath for Kondo spins and other quantum impurities within the numerical renormalization group method and other numerical approaches. In this short note we point out that Wilson chains can not serve as thermal reservoirs as their temperature changes by a number of order Delta E when a finite amount of energy Delta E is added. This proves that for a large class of non-equilibrium problems they cannot be used to predict the long-time behavior.