Quantum versus classical effects at zero and finite temperature in the quantum pyrochlore Yb$_2$Ti$_2$O$_7$

TL;DR

This study investigates the quantum and classical effects in the material Yb$_2$Ti$_2$O$_7$, revealing how quantum mechanics influence phase transitions, specific heat, and phase diagrams at finite temperatures.

Contribution

It combines finite temperature Lanczos and classical Monte Carlo methods to elucidate quantum effects on phase boundaries and thermodynamics in Yb$_2$Ti$_2$O$_7$, advancing understanding of quantum spin ice behavior.

Findings

Quantum effects shift phase boundaries and explain experimental discrepancies.

The material exhibits significant renormalization effects affecting its phase diagram.

A qualitative link between ferromagnetism and classical ice manifold explains its magnetic phases.

Abstract

We study the finite temperature properties of the candidate quantum spin ice material Yb$_2$Ti$_2$O$_7$ within the framework of an anisotropic nearest-neighbor spin $1/2$ model on the pyrochlore lattice. Using a combination of finite temperature Lanczos and classical Monte Carlo methods, we highlight the importance of quantum mechanical effects for establishing the existence and location of the low-temperature ordering transition. We perform simulations of the 32 site cluster, which capture the essential features of the specific heat curve seen in the cleanest known samples of this material. Focusing on recent experimental findings on Yb$_2$Ti$_2$O$_7$ [A. Scheie et al., Phys. Rev. Lett. 119, 127201 (2017) and J. D. Thompson et al., Phys. Rev. Lett. 119, 057203 (2017)], we then address the question of how the phase boundary between the ferromagnetic and paramagnetic phases changes when subjected to a magnetic field. We find that the quantum calculations explain discrepancies observed with a completely classical treatment and show that Yb$_2$Ti$_2$O$_7$ displays significant renormalization effects, which are at the heart of its reentrant lobed phase diagram. Finally, we develop a qualitative understanding of the existence of a ferromagnet by relating it to its counterpart that exists in the vicinity of the classical ice manifold.