Quantum Fisher Information Reveals Thermal and Dynamical Properties in Frustrated Magnets and Spin Ice Systems

The behaviour of magnetic materials presents a continuing challenge for physicists, and understanding their complex properties requires innovative measurement techniques. Chengkang Zhou from The University of Hong Kong, Zhengbang Zhou from University of Toronto, Félix Desrochers, and colleagues now demonstrate the power of Quantum Fisher Information (QFI) as a new tool to probe these materials. Their research focuses on quantum spin ice, a fascinating state of matter exhibiting exotic magnetic behaviour, and reveals how QFI responds to changes in temperature and magnetic order. The team’s calculations show that QFI effectively distinguishes between different magnetic phases and identifies critical points in the material’s behaviour, offering a sensitive method to characterise thermal and dynamical properties, and potentially aiding the interpretation of experiments on real materials like cerium-based pyrochlore systems.

This work focuses on understanding quantum spin liquids, materials where magnetic moments fluctuate even at very low temperatures, and utilizes neutron scattering experiments to investigate their complex behavior. The goal is to provide a way to experimentally determine the extent of entanglement within these exotic materials, revealing crucial details about their underlying quantum state. Quantum spin liquids are of great interest because they can host emergent particles and potentially be used for quantum computation.

Entanglement depth, a measure of how many spins are interconnected, is a key characteristic of these materials. The QFI serves as a powerful tool to quantify this entanglement by analyzing the sensitivity of the system to perturbations, allowing researchers to gain insights into the material’s quantum state. The team rigorously derived mathematical bounds on the QFI, connecting it directly to the number of entangled spins. This allows researchers to estimate the entanglement depth by measuring the neutron scattering cross-section, a quantity accessible through experiment. These calculations provide a theoretical framework for interpreting experimental data and extracting meaningful information about the entanglement within the material. The results demonstrate that the derived QFI bounds provide a way to experimentally quantify entanglement in quantum spin liquids. This work demonstrates that the QFI serves as a sensitive probe of both thermal and dynamical properties within these magnetic materials, revealing characteristic energy scales of phase transitions. The team employed advanced computational techniques, including multi-directed loop update Monte Carlo and exact diagonalization, to compute the QFI and calibrate theoretical models. Spin ice materials exhibit unusual magnetic behavior, hosting fractionalized quasiparticles and emergent photons.

Understanding the different phases of spin ice is crucial for unlocking their potential for future technologies. The QFI serves as a powerful tool to distinguish between these phases by analyzing the material’s underlying quantum state and identifying the boundaries between different phases. The team developed a new computational algorithm to accurately simulate the complex behavior of spin ice, allowing for efficient calculations of the QFI and providing a detailed map of the material’s phase diagram. Results demonstrate that the QFI clearly distinguishes between the ferromagnetic ordered phase, the thermal critical region, and two distinct spin ice phases, zero-flux and π-flux.

Heat maps of the QFI density reveal how this measure changes with both temperature and the strength of interactions within the material. The findings confirm the presence of two crossover temperature scales, one marking the transition from a simple paramagnetic state to classical spin ice, and a lower temperature crossover indicating the emergence of the quantum spin ice phase. This work provides a detailed picture of the material’s behavior and offers valuable insights into the complex interplay between quantum fluctuations and thermal effects.