Nanotechnology Now - Press Release: HKU physicists uncover hidden order in the quantum world through deconfined quantum critical points

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Figure 1. (A) Lattice model for realising the deconfined quantum phase transition. (B) The phase diagram for the square lattice SU(N) model. Dots represent the quantum phase transition points. Red points are those not compatible with a continuous phase transition and blues points are those consistent with conformal field theories, i.e., candidates for genuine DQCP. Credit The University of Hong Kong

Abstract:
In the intricate world of quantum physics, where particles interact in ways that seem to defy the standard rules of space and time, lies a profound mystery that continues to captivate scientists: the nature of deconfined quantum critical points (DQCPs). These elusive critical phenomena break away from the conventional framework of physics, offering a fascinating glimpse into a realm where quantum matter behaves in ways that challenge our classical understanding of the fundamental forces shaping the universe.

HKU physicists uncover hidden order in the quantum world through deconfined quantum critical points

Hong Kong, China | Posted on April 25th, 2025

us phase transitions (which are smooth and gradual) or first-order transitions (which are sudden and abrupt). Understanding DQCPs could provide new insights into how particles interact and how exotic states of matter emerge.

The Key to the Mystery: Entanglement Entropy
At the heart of this new study lies the concept of entanglement entropy, a measure of how particles in quantum systems are interrelated. It provides a way to quantify the amount of information shared between different parts of a system. Entanglement entropy offers a glimpse into the hidden structure of quantum systems, serving as a fundamental tool for probing quantum matter and understanding the nature of complex interactions that emerge at critical points.

Using advanced quantum Monte Carlo simulations (a computational method for modelling quantum systems) and rigorous theoretical analysis, researchers examine the behaviour of entanglement entropy in square-lattice SU(N) spin models — a theoretical framework designed to capture the essence of DQCPs.

Their meticulous computations revealed something extraordinary: at small value N (a parameter that determines the symmetry of the system), the behaviour of entanglement entropy deviated from expectations for smooth, continuous phase transitions. Instead, they found that DQCPs exhibit anomalous logarithmic behaviors, defyingthe theoretical constraints typically associated with continuous phase transitions.

The Breakthrough: A Critical Threshold and Conformal Fixed Points
One of the most striking revelations of the study was the identification of a critical threshold value of N. When N exceeds this threshold, DQCPs exhibit behaviours consistent with conformal fixed points — a mathematical framework that describes smooth, continuous phase transitions. This discovery is significant because it suggests that, under certain conditions, DQCPs can resemble continuous phase transitions. At these critical points, the system aligns with conformal fixed points, revealing a hidden structure in the quantum world where the boundaries between distinct phases dissolve, and matter exists in a state of extraordinary fluidity, defying the usual rules of physics.

Why This Matters
The implications of these findings are profound. DQCPs provide a unique testing ground for exploring the interplay of quantum mechanics, symmetry, and critical phenomena. Understanding their nature could unlock new insights into:

Exotic States of Matter: DQCPs are believed to be connected to the emergence of exotic phases, such as quantum spin liquids, which have potential applications in quantum computing and other advanced technologies.
Fundamental Physics: By challenging the traditional Landau paradigm, DQCPs force us to rethink the principles that govern phase transitions, potentially leading to new theoretical frameworks.
Technological Innovation: Insights gained from studying DQCPs could inform the design of novel materials with unique quantum properties, such as high-temperature superconductors or quantum magnets.
Conclusion
The enigmatic world of deconfined quantum critical points stands at the frontier of modern physics, offering a glimpse into the uncharted territory of quantum mechanics. Through their meticulous investigation of entanglement entropy and SU(N) spin models, researchers have made significant strides in unravelling the mysteries of these critical phenomena.

This study was conducted in collaboration with Dr Jiarui ZHAO from the Chinese University of Hong Kong, Professor Meng CHENG from Yale University, Professor Cenke XU from the University of California, Santa Barbara, Professor Michael M. SCHERER from Ruhr-University Bochum, and Professor Lukas JANSSEN from TU Dresden.