Dicke-ising Chain Analysis Achieves Improved Accuracy in Magnetically Ordered Phases with NLCE+DMRG

Understanding the interplay between light and matter is fundamental to many areas of physics, and recent research focuses on the Dicke-Ising chain, a model system exhibiting collective behaviour. J. Leibig, M. Hörmann, and A. Langheld, alongside colleagues at various institutions, have developed a quantitative approach utilising numerical linked-cluster expansions combined with density matrix renormalization group calculations to analyse this complex system. Their work demonstrates that the Dicke-Ising chain can be accurately described by an effective self-consistent matter Hamiltonian, simplifying the analysis and eliminating the need to account for photon-spin correlations. This advancement allows for a significantly more precise determination of the phase diagram, refining estimates of critical points and confirming the existence of previously theorised phases. The research provides a detailed understanding of superradiant phase transitions and establishes a clear link between the Dicke-Ising model and the well-known transverse-field Ising model.

The research team achieved a precise determination of the phase diagram for this system by mapping it onto an effective self-consistent matter Hamiltonian, effectively decoupling the photon field and treating it as a constant influence on the material components. This innovative technique eliminates the need to account for correlations between photons and spins, simplifying the analysis and enabling highly accurate calculations. Experiments show that this method significantly improves the accuracy of identifying magnetically ordered phases compared to previous theoretical estimates.

The study unveils a powerful combination of numerical linked-cluster expansions and density matrix renormalization group calculations (NLCE+DMRG) to solve the resulting matter Hamiltonian. This computational strategy allows for a detailed examination of the quantum phase transitions within the Dicke-Ising chain, particularly refining the location of the multicritical point governing the superradiant phase transition with a relative accuracy of 10−4 for ferromagnetic interactions. For antiferromagnetic interactions, the team confirms the existence of a narrow antiferromagnetic superradiant phase, a previously predicted but challenging-to-verify state of matter. The work opens new avenues for exploring complex quantum systems by focusing on the essential material properties.

This breakthrough reveals that the antiferromagnetic superradiant phase can be understood as the ground state of an antiferromagnetic transverse-field Ising model with a longitudinal field. The research establishes that this phase emerges through a continuous condensation of polaritons, followed by a first-order transition into a paramagnetic superradiant phase, providing a clear pathway for its formation. By solving the self-consistent effective matter Hamiltonian, NLCE+DMRG provides a precise determination of the Dicke-Ising phase diagram in one dimension, offering a robust framework for future investigations. The implications of this work extend to various fields, including cavity quantum electrodynamics and the development of quantum simulators. Understanding the interplay between light and matter at this fundamental level is crucial for designing and controlling quantum devices, potentially leading to advancements in quantum computing and sensing technologies. The ability to accurately predict and manipulate the phase transitions in the Dicke-Ising chain paves the way for creating novel quantum materials with tailored properties and functionalities, promising exciting possibilities for future research and applications.

Dicke-Ising Model via Matter Hamiltonian Mapping

The research detailed a novel methodological approach to understanding the Dicke-Ising model, a system describing the collective interaction of light and matter. Scientists engineered a pathway to bypass the need for complex photon-spin correlation calculations by mapping the Dicke-Ising chain onto a self-consistent effective matter Hamiltonian, effectively treating the photon field as a static influence. This innovative framework allowed the team to focus solely on solving the resulting matter Hamiltonian, significantly simplifying the analysis of the system’s phase diagram. To achieve this, the study pioneered a combination of numerical linked-cluster expansions (NLCE) and density matrix renormalization group (DMRG) calculations.

The NLCE method was employed to accurately determine the properties of the system in one dimension, while DMRG served as a powerful tool for solving the complex self-consistent matter Hamiltonian. Specifically, the team refined the location of the multicritical point for ferromagnetic Ising couplings, achieving a relative accuracy of 0.01. This precision represents a substantial improvement over previous estimations and highlights the efficacy of the combined NLCE+DMRG technique. For antiferromagnetic Ising couplings, the research confirmed the existence of a narrow antiferromagnetic superradiant phase, validating theoretical predictions.

The effective matter Hamiltonian framework identified this phase as the ground state of an antiferromagnetic transverse-field Ising model with a longitudinal field, revealing its emergence through a continuous Dicke-type polariton condensation. This condensation is then followed by a first-order transition into a paramagnetic superradiant phase, demonstrating a clear pathway for phase transitions within the system. The NLCE+DMRG approach delivers a precise determination of the Dicke-Ising phase diagram in one dimension, offering a robust and accurate method for exploring complex light-matter interactions and providing a foundation for future investigations into related quantum systems. This methodological advancement enables a deeper understanding of collective phenomena in cavity-QED, circuit-QED, and other platforms where light and matter are strongly coupled.

Dicke-Ising Phase Diagram Mapped with High Precision

Scientists achieved a precise determination of the Dicke-Ising phase diagram in one dimension through a novel application of numerical linked-cluster expansions combined with density matrix renormalization group calculations (NLCE+DMRG). The research focused on solving the self-consistent effective matter Hamiltonian resulting from mapping the Dicke-Ising chain onto an effective model, bypassing the need for complex photon-spin correlation calculations. Experiments revealed magnetically ordered phases with significantly improved accuracy compared to prior estimations, establishing a new benchmark for understanding collective light-matter interactions. For ferromagnetic Ising couplings, the team measured the location of the multicritical point governing the superradiant phase transition with a relative accuracy of .

This breakthrough delivers a refined understanding of the transition between different ordered phases within the system. Data shows that the NLCE+DMRG method accurately pinpoints the point at which the nature of the superradiant transition changes, offering crucial insights for controlling and manipulating these quantum systems. The work confirms the existence of a narrow antiferromagnetic superradiant phase in the limit, a previously theorized state with unique properties. Measurements confirm that this antiferromagnetic superradiant phase corresponds to the many-body ground state of an antiferromagnetic transverse-field Ising model with a longitudinal field.

Results demonstrate that this phase emerges through a continuous Dicke-type polariton condensation from the antiferromagnetic normal phase, followed by a first-order transition into the paramagnetic superradiant phase. Tests prove that the NLCE+DMRG approach provides a precise determination of the phase boundaries, enabling detailed characterization of the quantum states and transitions within the Dicke-Ising model. This advancement has implications for designing novel quantum simulators and exploring collective phenomena in cavity-QED and circuit-QED platforms.

Dicke-Ising Chain Phase Diagram Precisely Determined

This work presents a precise determination of the phase diagram for the one-dimensional Dicke-Ising chain, building upon the established mapping of the Dicke model to an effective matter Hamiltonian. By treating the photon field as a self-consistent parameter, researchers circumvented the need to model photon-spin correlations, simplifying the analysis and enabling accurate calculations of magnetically ordered phases. The application of numerical linked-cluster expansions combined with density matrix renormalization group calculations, NLCE+DMRG, allowed for a refined understanding of the system’s behaviour. Specifically, the study accurately located the multicritical point governing the superradiant phase transition for ferromagnetic interactions, achieving a relative accuracy of one percent.

For antiferromagnetic interactions, the existence of a narrow antiferromagnetic superradiant phase was confirmed, and its origin identified as stemming from an antiferromagnetic transverse-field Ising model. The authors acknowledge limitations inherent in the numerical methods employed, particularly concerning finite-size effects and computational cost. Future research could explore the extension of this framework to higher dimensions or the inclusion of additional complexities, such as long-range interactions, to further refine the understanding of collective light-matter interactions in these systems.