Scaling theory vs exact numerical results for spinless resonant level model

TL;DR

This paper uses quantum Monte Carlo simulations to analyze the interacting resonant level model, revealing how scaling theories compare with exact numerical results across different interaction strengths, with implications for heavy-fermion materials.

Contribution

It provides a detailed numerical validation of scaling formulas for the IRLM across a wide interaction range, highlighting their accuracy and limitations.

Findings

Excellent agreement with scaling for negative Ufc including quantum critical point

Deviations from scaling occur at large positive Ufc

Results are relevant to heavy-fermion compounds like Samarium materials

Abstract

The continuous-time quantum Monte Carlo method is applied to the interacting resonant level model (IRLM) using double expansion with respect to Coulomb interaction Ufc and hybridization V. Thermodynamics of the IRLM without spin is equivalent to the anisotropic Kondo model in the low-energy limit. Exact dynamics and thermodynamics of the IRLM are derived numerically for a wide range of Ufc with a given value of V. For negative Ufc, excellent agreement including a quantum critical point is found with a simple scaling formula that deals with V in the lowest-order, and Ufc up to infinite order. As Ufc becomes positive and large, lower order scaling results deviate from exact numerical results. Possible relevance of the results is discussed to certain Samarium compounds with unusual heavy-fermion behavior.