Extracting precise critical exponents from quantum systems at experimentally accessible scales presents key challenges due to slow correlation times and photon loss influencing behaviour. A unified framework resolves static and dynamic critical scaling in both closed and open quantum systems using the Dicke model, enabling analysis previously obscured by finite size effects. An analytical method improves characterisation of phase transitions, points where materials change properties, at scales relevant to experiments.

Standard techniques struggle when systems are small or affected by external factors influencing these changes; this new framework addresses those limitations effectively. The work confirms existing theories about how such shifts occur within complex quantum systems losing energy, offering insights applicable across physics disciplines. Researchers at Tsinghua University have developed an analytical framework characterising phase transitions within quantum systems experiencing energy loss; these shifts represent points where materials alter their properties.

Understanding how quickly those changes occur requires determining ‘critical exponents’, numbers describing this rate of change, imagine zooming in on a colour transition to see if it’s a sharp line or gradual fade. The team focused on the Dicke model, which represents atoms interacting strongly with light like many tiny antennae responding together, allowing them to analyse behaviour previously obscured by system size limitations.

This new approach accounts for both static conditions and dynamic processes, verifying established theories about energy dissipation while offering broader applications across physics disciplines. However, extracting precise values remains challenging at experimentally accessible scales due to slow responses and photon loss.

Dynamic ramping enhances critical exponent determination

Scientists have achieved unprecedented accuracy when extracting critical exponents from dynamic ramping data, reducing uncertainty by over thirty percent compared to static measurements alone. Their breakthrough stems from a unified framework analysing both open and closed Dicke models, systems describing collective light-matter interactions, at mesoscopic scales where traditional methods struggle with slow correlation times and photon loss. The team successfully incorporated leading irrelevant corrections into a scaling protocol, enabling accurate parameter extraction even in realistically sized experiments exhibiting finite size effects that previous analyses could not reliably address.

Extending this analysis to open systems incorporating photon loss then extracted a value of 2·023 for ν when analysing ramping dynamics under dissipation rates varying from 0·1 to three. Examining how quickly parameters change with ramp speed, specifically quadratic responses, resulted in an exponent μ equal to 0·989 which closely matches theoretical predictions based on large-N approximations.

Mapping Quantum State Transitions via Large-N Expansion and Mesoscopic Scaling

A large-N analysis, simplifying calculations by focusing on collective behaviour in systems with many interacting components, was employed to pinpoint specific ‘fixed points’ within both closed and open versions of the Dicke model; this is analogous to identifying stable configurations in a complex system. This technique mapped out quantum state transitions depending on factors like light-matter coupling strength and energy dissipation as illustrated through diagrams showing distinct universality classes. A mesoscopic scaling framework systematically accounts for “irrelevant corrections”, minor effects typically ignored but important when dealing with realistically sized experiments impacted by finite size limitations.

Unifying analysis of quantum transitions via limited correction incorporation

Methods refining our understanding of how quantum systems transition between states represent a step towards controlling complex materials and harnessing their properties. While analyses now unify both isolated and energy-dissipating systems using the Dicke model, representing atoms interacting with light, calculations currently rely on incorporating only ‘leading’ irrelevant corrections, often overlooked in simpler models yet crucial to examining realistic experimental scales. Acknowledging this limitation is important as real experiments involve more complex influences potentially shifting precise values. By extending mesoscopic scaling to include dynamic processes alongside static measurements, Kibble-Zurek scaling was verified; this theory describes defect formation during rapid system changes while clarifying competing influences of factors like ramp speed upon these transitions.

The research successfully identified distinct stable configurations within both closed and open versions of the Dicke model using a large-N analysis. This work provides a unified framework for understanding how quantum systems transition between states, accounting for effects typically ignored in simpler models but relevant at experimentally accessible sizes. Measurements utilising ramping dynamics yielded an exponent of 0·989, closely aligning with theoretical predictions. The study verifies Kibble-Zurek scaling and clarifies competition between finite size, dissipation, and ramp speed during dynamic transitions.

👉 More information
🗞 Kibble–Zurek Scaling in the Dicke Model at Mesoscopic Scales
✍️ Haowei Li and Hanteng Wang
🧠 ArXiv: https://arxiv.org/abs/2608.20067

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