# Effects of an Additional Conduction Band on Singlet-Antiferromagnet Competition in the Periodic Anderson Model

## TL;DR

This study investigates how adding an extra conduction band influences antiferromagnetic order and quantum criticality in the Periodic Anderson Model, revealing stabilization of AF order and changes in spectral functions through mean field theory and quantum Monte Carlo simulations.

## Contribution

It introduces the effects of an additional conduction band on magnetic phases and quantum critical points in the Periodic Anderson Model using combined mean field and quantum Monte Carlo methods.

## Key findings

- Additional band stabilizes AF order at half-filling.
- Quantum Monte Carlo confirms AF stabilization via RKKY interaction.
- Spectral functions provide insight into AF-singlet competition.

## Abstract

The competition between antiferromagnetic (AF) order and singlet formation is a central phenomenon of the Kondo and Periodic Anderson Hamiltonians, and of the heavy fermion materials they describe. In this paper, we explore the effects of an additional conduction band on magnetism in these models, and, specifically, on changes in the AF-singlet quantum critical point (QCP) and the one particle and spin spectral functions. To understand the magnetic phase transition qualitatively, we first carry out a self-consistent mean field theory (MFT). The basic conclusion is that, at half-filling, the coupling to the additional band stabilizes the AF phase to larger $f$ $d$ hybridization $V$ in the PAM. We also explore the possibility of competing ferromagnetic phases when this conduction band is doped away from half-filling. We next employ Quantum Monte Carlo (QMC) which, in combination with finite size scaling, allows us to evaluate the position of the QCP using an exact treatment of the interactions. This approach confirms the stabilization of AF order, which occurs through an enhancement of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. QMC results for the spectral function $A(\textbf{q},\omega)$ and dynamic spin structure factor $\chi(\textbf{q},\omega)$ yield additional insight into the AF-singlet competition and the low temperature phases.