Quantum criticality in the spin-isotropic pseudogap Bose-Fermi Kondo model: entropy, scaling, and the g-theorem

TL;DR

This paper investigates the entropy behavior and quantum phase transitions in the pseudogap Bose-Fermi Kondo model using a large-N approach, revealing the breakdown of the g-theorem due to anomalous scaling contributions.

Contribution

It provides a detailed analysis of entropy scaling and phase transitions in the pseudogap Bose-Fermi Kondo model, showing the g-theorem's inapplicability at the large-N level.

Findings

The g-theorem does not hold for the model at large N.

Anomalous contributions affect entropy scaling in the hydrodynamic regime.

Comparison with Sachdev-Ye-Kitaev model highlights unique features.

Abstract

We study the behavior of the entropy of the pseudogap Bose-Fermi Kondo model within a dynamical large-$N$ limit, where $N$ is related to the symmetry group of the model. This model is a general quantum impurity model that describes a localized level coupled to a fermionic bath having a density of states that vanishes in a powerlaw fashion near the Fermi energy and to a bosonic bath possessing a powerlaw spectral density below a cutoff energy. As a function of the couplings to the baths various quantum phase transitions can occur. We study how the impurity entropy changes across these zero-temperature transitions and compare our results with predictions based on the g-theorem. This is accomplished by an analysis of the leading and sub-leading scaling behavior. Our analysis shows that the $g$-theorem does not apply to the pseudogap Bose-Fermi Kondo model at the large-N level. This inapplicability originates from an anomalous contribution to the scaling function in the hydrodynamic regime where $k_B T>\hbar \omega$ which is absent in the quantum coherent regime, i.e., for $k_B T<\hbar \omega$. We also compare our results with those obtained for the Sachdev-Ye-Kitaev model.