Quantum Phase Transition of a Magnet in a Spin Bath

TL;DR

This study investigates how hyperfine interactions with nuclear spins influence the quantum critical behavior in LiHoF$_4$, revealing that nuclear spin baths limit the entanglement length scale and affect the electronic excitation spectrum near the quantum phase transition.

Contribution

It demonstrates that nuclear spin interactions prevent the expected electronic mode softening at the quantum critical point, highlighting a fundamental limit imposed by the nuclear spin bath.

Findings

Hyperfine coupling forestalls electronic mode softening.

Nuclear spins control entanglement length scale.

Limits approach to electronic quantum criticality.

Abstract

The excitation spectrum of a model magnetic system, LiHoF$_4$, has been studied using neutron spectroscopy as the system is tuned to its quantum critical point by an applied magnetic field. The electronic mode softening expected for a quantum phase transition is forestalled by hyperfine coupling to the nuclear spins. We show that interactions with the nuclear spin bath control the length scale over which the excitations can be entangled. This generic result limits how far it is possible to approach intrinsic electronic quantum criticality.