Novel Quantum Model Reveals Stable States Defying Conventional Phase Transitions

Researchers are increasingly interested in understanding how dissipation affects quantum phase transitions. Jun-Ling Wang, Jiong Li, and Qing-Hu Chen from Zhejiang University, alongside et al., have investigated dissipative phase transitions within the Dicke-Ising model, a framework combining spin interactions with light-matter coupling. Their work, utilising a mean-field approach and stability analysis, demonstrates that dissipation significantly alters the phase diagram, stabilising bistable nonequilibrium states in the longitudinal Dicke-Ising model where such transitions are otherwise absent. This conversion of a triple point into a tetracritical point highlights the complex interplay between spin interactions, light-matter coupling and dissipation, offering a theoretical basis for exploring nonequilibrium physics in solid-state systems and providing broad tunability of the phase diagram.

This work details investigations into the Dicke-Ising model, a framework combining collective atomic interactions with individual spin properties, revealing how energy loss, or dissipation, can induce unique, stable states not found in equilibrium conditions.

Specifically, the study focuses on two variations of the model: a transverse version where spins interact via their x-axis, and a longitudinal version where interactions occur along the z-axis. Through a mean-field approach and rigorous stability analysis, scientists have mapped out the resulting phase diagrams, demonstrating that dissipation significantly impacts the system’s behaviour.

While dissipation causes only a slight shift in the phase diagram of the transverse Dicke-Ising model compared to its equilibrium counterpart, the longitudinal model exhibits far more dramatic changes. Dissipation in the longitudinal configuration stabilizes bistable, nonequilibrium steady states and triggers first-order phase transitions absent in the ground-state scenario.

This bistable phase is characterised by the simultaneous presence of superradiant, where atoms collectively emit light, and antiferromagnetic, where neighbouring spins align in opposite directions, orders. Notably, the research demonstrates that a ground-state triple point, representing a convergence of different phases, is transformed into a tetracritical point under these conditions.

A tetracritical point signifies the intersection of boundaries between first- and second-order transitions, indicating a fundamental shift in the system’s response to external parameters. These findings highlight that the combined effects of spin interactions, light-matter coupling, and dissipation support a diverse range of nonequilibrium phase transitions and offer substantial control over the system’s phase diagram.

This theoretical work provides a foundation for exploring nonequilibrium physics in realistic, open solid-state quantum systems, potentially paving the way for new designs and control mechanisms in quantum technologies. The ability to tune and stabilise these unique phases through dissipation opens exciting possibilities for manipulating quantum states and developing advanced quantum materials.

Dissipative dynamics and phase transitions in the Dicke-Ising model

Mean-field analysis underpinned the investigation of dissipative phase transitions within the open transverse and longitudinal Dicke-Ising model (DIM). This work began with establishing the ground-state phase diagrams for both models to provide a baseline for comparison with the dissipative regimes. The transverse DIM exhibited a phase diagram only slightly shifted upwards when compared to its ground-state equivalent, indicating a limited impact from dissipation on this configuration.

In contrast, detailed stability analysis revealed that dissipation within the longitudinal DIM fundamentally altered the phase behaviour, stabilising bistable nonequilibrium steady states and inducing first-order phase transitions not present in the ground-state diagram. This bistable phase was characterised by the simultaneous coexistence of superradiant and antiferromagnetic orders, transforming a ground-state triple point into a tetracritical point where first- and second-order transition boundaries converged.

The research employed a mean-field approach to derive the dissipative phase diagrams, systematically exploring the interplay between spin interactions, light-matter coupling, and dissipation. Steady-state solutions were obtained by solving the relevant equations of motion, and their stability was rigorously assessed through linear stability analysis, ensuring the identified phases were genuinely stable nonequilibrium states. This methodology allowed for the precise mapping of phase boundaries and the identification of novel phases arising from the combined effects of dissipation and interactions, offering a theoretical framework for understanding nonequilibrium physics in solid-state systems.

Dissipative dynamics induce bistability and tetracriticality in the longitudinal Dicke-Ising model

Researchers investigated dissipative phase transitions within the open transverse and longitudinal Dicke-Ising model using a mean-field approach and stability analysis. Dissipation in the transverse Dicke-Ising model resulted in a phase diagram only slightly shifted upwards when compared to the ground-state counterpart.

However, dissipation within the longitudinal Dicke-Ising model stabilised bistable nonequilibrium steady states and induced first-order phase transitions not present in the ground-state diagram. This bistable phase is characterised by the simultaneous coexistence of superradiant and antiferromagnetic orders, transforming a ground-state triple point into a tetracritical point where first- and second-order transition boundaries intersect.

The study reveals that the interplay between spin interactions, light-matter coupling, and dissipation supports a diverse range of nonequilibrium phase transitions and provides broad tunability of the phase diagram. Specifically, the research demonstrates the emergence of genuinely nonequilibrium effects induced by dissipation in the longitudinal model, a phenomenon absent in the transverse configuration.

This work establishes a theoretical foundation for exploring nonequilibrium physics within realistic open solid-state quantum systems. The Dicke-Ising model combines a Dicke Hamiltonian with Ising-type spin-spin interactions, unifying photon-mediated long-range coherence with interaction-driven local correlations.

Mean-field predictions largely govern the overall phase behaviour, while theories beyond mean field provide quantitative tuning to phase boundaries. Existing studies have primarily focused on the dissipative dynamics of the pure Dicke model, creating an imbalance in theoretical understanding compared to experimental progress. The research addresses this gap by investigating dissipative phase transitions in the Dicke-Ising model, considering both dissipation and Ising interactions as crucial factors.

Longitudinal coupling drives bistability and tetracriticality in the dissipative Dicke-Ising model

Dissipative phase transitions within the Dicke-Ising model reveal how interactions between spins, light-matter coupling, and energy dissipation collectively influence the resulting phase structure. Investigations utilising a mean-field approach and stability analysis demonstrate distinct behaviours between transverse and longitudinal configurations of the model.

Dissipation in the transverse Dicke-Ising model causes a slight upward shift in the phase diagram, mirroring behaviour observed in simpler Dicke models. However, the longitudinal Dicke-Ising model exhibits a more dramatic response to dissipation, stabilising bistable, non-equilibrium steady states and inducing first-order phase transitions not present in the ground state.

These bistable states are characterised by the simultaneous presence of superradiant and antiferromagnetic order, transforming a triple point into a tetracritical point where different types of phase transitions converge. This reshaping of the phase diagram highlights that dissipation does not simply alter existing boundaries but can fundamentally change the nature of phase transitions.

The authors acknowledge their analysis relies on a mean-field treatment, but suggest the observed bistability and first-order transitions are likely robust even beyond this approximation. The Dicke-Ising model therefore offers a valuable theoretical framework for investigating non-equilibrium physics in solid-state systems where both strong light-matter coupling and spin interactions are prevalent.