# Determinant Quantum Monte Carlo Study of Exhaustion in the Periodic Anderson Model

## TL;DR

This study uses determinant Quantum Monte Carlo to investigate how dilution affects the transition point between singlet formation and antiferromagnetic order in the Periodic Anderson model, providing insights into exhaustion physics.

## Contribution

It introduces a sign-problem-free variant of the Periodic Anderson model to explore the impact of conduction electron dilution on magnetic phase transitions.

## Key findings

- Dilution shifts the critical hybridization V for the singlet-antiferromagnetic transition.
- The study demonstrates the feasibility of low-temperature QMC simulations for diluted models.
- Results offer new understanding of exhaustion effects in heavy fermion systems.

## Abstract

The Kondo and Periodic Anderson models describe many of the qualitative features of local moments coupled to a conduction band, and thereby the physics of materials such as the heavy fermions. In particular, when the exchange coupling $J$ or hybridization $V$ between the moments and the electrons of the metallic band is large, singlets form, quenching the magnetism. In the opposite, small $J$ or $V$, limit, the moments survive, and the conduction electrons mediate an effective interaction which can trigger long range, often antiferromagnetic, order. In the case of the Kondo model, where the moments are described by local spins, Nozi\`eres considered the possibility that the available conduction electrons within the Kondo temperature of the Fermi surface would be insufficient in number to accomplish the screening. Much effort in the literature has been devoted to the study of the temperature scales in the resulting `exhaustion' problem, and how the `coherence temperature' where a heavy Fermi liquid forms is related to the Kondo temperature. In this paper, we study a version of the Periodic Anderson model in which some of the conduction electrons are removed in a way which avoids the fermion sign problem and hence allows low temperature Quantum Monte Carlo simulations which can access both singlet formation and magnetic ordering temperature scales. We are then able to focus on a somewhat different aspect of exhaustion physics than previously considered: the effect of dilution on the critical $V$ for the singlet-antiferromagnetic transition.