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New Algorithm by HKU Physicists Solves Problem in Constrained Quantum Material Models

Image Credits: HKU, Press Release

The intrinsic scale limit of current quantum material hinders the possible development of technology, thus the discovery of a new generation of quantum materials holds the key to technological revolutions, such as stable topological quantum computers, high-temperature superconductors, high-capacity information and energy storage. Nevertheless, due to their nature of strongly correlated electrons, it is not uncommon for the next generation of quantum materials to have extremely complex interactions with the environment, making it difficult to study their properties and to make use of them.

Scientists are working proactively to learn how this next generation of quantum materials could reach and remain stable at the topological phase and how to make use of their excited particles. Recently, Postdoctoral Fellow Dr Zheng YAN and Associate Professor Dr Zi Yang MENG, from the Research Division for Physics and Astronomy of the Faculty of Science at the University of Hong Kong (HKU), have invented a new algorithm that could solve a large class of important constrained quantum material models, via powerful supercomputer combined with theoretical analysis.

They also teamed up with Dr Yancheng WANG from China University of Mining and Technology, Dr Nvsen MA from Beihang University, and Professor Yang QI from Fudan University to employ the algorithm and untangle a long-standing puzzle of a typical constrained quantum materials model, ‘quantum dimer model’.

Their study reveals the unique non-trivial interaction among ‘visons’, a mysterious particle that is excited in a topological order which carries finite emergent flux and uncovers the real property of this useful particle which may push the development of technological innovation. The research findings are recently published in the renowned academic journal npj Quantum Materials.

Discovery of topological excitations which carries long-range quantum entanglement

Using the new algorithm and from their simulations on the Tianhe-II supercomputer, the research team found clear quantum entangled excitations (scientifically called vison and dimer excitations) without the interference of high-energy excitation.

Vison is a mysterious particle that often appears in pairs and is difficult to detect a single vison in ordinary models. It is a kind of emergent article (anyons) excited in a topological order which carries finite emergent flux. Via the newly developed algorithm, the HKU team could compute the spectrums of single vison, dimer (coupled visons in the real model), vison-convolution (also known as VC; visons with weak interaction).

The research suggests that visons have binding energy in forming the dimer correlation and consequently their interaction effect is attractive and gives rise to a bound state with lower energy than the naive convolution. Through this study, they reveal the unique non-trivial interaction among the mysterious visons.

Furthermore, the research group also found emergent continuous symmetry at the phase transition from the topological phase to a solid phase in the model, it is clear a 4D sphere histogram and radius is conserved.

Through the simulation, researchers further saw that vison condenses on certain points on a four-dimensional sphere in the order parameter space to prove the results of the previous predictions made by theorists. This reveals the mechanism of vison condensation and critical point.

New algorithm brings new opportunity

This finding helps scientists to understand the behaviour and interaction of anyons in the topological order, which might have potential applications in future quantum information technologies.

With the powerful new algorithms and the unique properties of topological excitations discovered, many interesting research and potential applications with topological quantum materials can be pursued from here.

Dr Meng stated, “The new algorithm for constrained quantum models and their solutions of topological excitations will eventually bring benefits to society, such that these visons are the information carrier for quantum computation and quantum computers.

Our algorithm enables us to directly access numerical results with key theoretical predictions quantitatively, which is not possible before. Such efforts will certainly lead to more profound and impactful discoveries in quantum materials.”

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