Layered Spin Liquids Exhibit Diffusion and Relaxation of Topological Excitations Via Nonlinear Dynamics

The behaviour of exotic materials known as spin liquids presents a fundamental challenge to condensed matter physics, and understanding the dynamics of their unusual excitations is crucial to unlocking their potential. Aprem P. Joy, Roman Lange, and Achim Rosch from the Institute for Theoretical Physics, University of Cologne, investigate how these excitations move and interact within layered spin liquid materials. Their work reveals that the speed at which these excitations respond to external stimuli, such as a pulse of light, depends directly on the intensity of that stimulus, a surprising result with implications for experimental observation. The team demonstrates that excitation spreads into the material’s bulk in a unique way, either slowly and steadily or, if interactions between excitations are present, in a more complex, logarithmic fashion, offering a potential signature of topological order detectable through pump-probe experiments. This research provides new theoretical predictions for how to probe these elusive states of matter and could guide the development of future quantum technologies.

These materials host two-dimensional topological phases where fundamental particles can move freely within layers, but interactions between layers cause them to relax. The team developed a theoretical framework combining advanced mathematical techniques to describe how these excitations move and lose energy, revealing a new mechanism for momentum relaxation arising from interlayer interactions. The results demonstrate that the rate of relaxation depends on the strength of these interactions and the dimensionality of the excitations, offering insights into designing materials with tailored properties.

The study shows that these excitations spread subdiffusively into the bulk of the material when annihilation processes are absent, and propagation becomes linear when excitations are allowed to annihilate each other. Researchers used exact mathematical solutions and computer simulations to explore how pump-probe experiments can reveal the presence of these two-dimensional excitations in three-dimensional materials, linking the experiment timescale to the initial excitation density.

Kagome Lattices and Quantum Spin Liquid States

A comprehensive review of recent research highlights significant progress in understanding quantum spin liquids and topological order, particularly in materials with Kagome lattice structures. Many studies focus on identifying materials exhibiting quantum spin liquid behaviour and exploring experimental techniques to detect these exotic phases, including research into related concepts like Kitaev materials, which are predicted to host unusual excitations and topological properties.

A significant portion of the research explores fractons, particles with restricted movement, and the X-cube model, a prominent example. Scientists are working to understand the properties of these particles and their potential for creating new quantum phases, alongside investigations into topological insulators and their surface states, with potential applications in spintronics and the search for Majorana fermions.

Researchers employ a variety of experimental techniques, including Raman spectroscopy and neutron scattering, to probe magnetic excitations and identify quantum spin liquid phases. The thermal Hall effect, optical conductivity, and total internal reflection fluorescence microscopy are also used. A surprising connection emerges between condensed matter physics and the study of pattern formation and non-equilibrium physics.

Studies explore the dynamics of pattern formation in reaction-diffusion systems and the behaviour of materials under stress. The Kibble-Zurek mechanism, which describes the formation of topological defects during rapid phase transitions, may be relevant to understanding the formation of defects in quantum spin liquids and fracton systems. Researchers are investigating the potential to view fractons as a generalization of dislocations with restricted mobility, utilizing advanced mathematical tools such as renormalization group methods and field theory.

Several key observations emerge from this research. The role of topological defects, such as dislocations, in quantum materials is a recurring theme, and understanding their dynamics and impact on material properties is crucial. The study of non-equilibrium dynamics and the application of concepts from pattern formation may provide new insights, and identifying unambiguous experimental signatures of quantum spin liquids, fractons, and other topological phases remains a major challenge. Bridging the gap between condensed matter physics and other fields could lead to exciting new discoveries.

Excitations’ Subdiffusive Spread and Logarithmic Decay

This research details how the dynamics of topological excitations within layered materials can be investigated using pump-probe experiments. The team demonstrates that the timescale of these experiments is linked to the intensity of the initial excitation, revealing a subdiffusive spread of excitation into the material’s bulk when annihilation processes are absent. When pair-annihilation is permitted, the propagation becomes logarithmic, and the overall density decays at a slower rate.

Furthermore, the study shows that the presence of screw dislocations effectively creates pathways for single-particle diffusion between layers, overcoming the usual restriction of pair-wise movement. This is because dislocations act as connections between layers, allowing excitations to move freely in three dimensions. The researchers used mathematical solutions and modelling to predict the behaviour of these excitations and to determine how pump-probe experiments can be used to measure their properties.