Dicke-ising Model Study Confirms Superradiant and Antiferromagnetic Order, Resolving Discrepancies in Previous Investigations

Recent investigations into the behaviour of interacting quantum systems have sparked debate regarding the emergence of superradiance, a phenomenon where collective emission of light amplifies significantly. Max Hörmann, Anja Langheld, and Jonas Leibig, alongside colleagues from Friedrich-Alexander-Universität Erlangen-Nürnberg, address a specific discrepancy arising from recent work on the Dicke-Ising model. The team demonstrates that features previously questioned, namely, the coexistence of superradiant behaviour with antiferromagnetic order and a particular ordering of spectral lines, are, in fact, present within the model’s established parameter range. This clarification advances understanding of collective quantum phenomena and resolves a critical point of contention in the field, offering a more complete picture of how light and matter interact at the quantum level.

In their recent article, Mendonça et al present a novel numerical approach to tackle one-dimensional composite light-matter systems, utilizing a variational unitary transformation accompanied by density matrix renormalization group calculations to map out the quantum phase diagram of Dicke-spin models. This work investigates the presence of both ferromagnetic and antiferromagnetic order, alongside changes in the position of some phase transition lines observed in other studies, demonstrating that both features are indeed present within the Dicke-Ising model for the investigated parameter range.

Quantum Monte Carlo Validates Superradiant Phase Existence

This work presents strong evidence for previously missed features of the quantum phase diagram, namely, the existence of an intermediate antiferromagnetic superradiant phase and a change in the order of phase transitions for ferromagnetic Ising interactions. The team’s calculations reveal that previous studies may have overlooked these features due to limitations in system size and resolution. For antiferromagnetic interactions, the team confirms an intermediate phase with coexisting antiferromagnetic order and superradiance, a finding quantitatively verified by quantum Monte Carlo simulations with up to N = 8192 spins. This intermediate phase is relatively limited in one dimension, potentially explaining why it was not identified in earlier calculations.

The quantum phase transition from the normal to the intermediate phase is second order, as supported by exact solutions of the low-energy spectrum and verified by quantum Monte Carlo methods. In the realm of ferromagnetic interactions, the team demonstrates that the transition to the superradiant phase is first order when approaching a vanishing longitudinal magnetic field, a result predicted by Landau theory and confirmed by an exact self-consistent approach. This first-order transition persists for sufficiently small magnetic fields, as confirmed by quantum Monte Carlo simulations, and changes at a multi-critical point at J ≈ ε/2 = 0. 5. The team’s findings suggest that the first-order transition line lies outside the parameter regime explored in previous studies, offering a plausible explanation for discrepancies.

New Magnetic and Superradiant Phase Discovered

This work presents compelling evidence for previously overlooked phases within the Dicke-Ising model, a system describing the interaction of light and matter. Scientists achieved detailed quantum Monte Carlo simulations, utilizing system sizes up to N = 8192 spins, to map the phase diagram of this model with unprecedented precision. Results demonstrate the existence of an intermediate phase exhibiting both magnetic and superradiant order in the antiferromagnetic Dicke-Ising chain, a feature absent in prior analyses. Specifically, the team identified this phase and precisely characterized its boundaries, revealing its limited extent in one dimension but broader presence in higher dimensions.

Further investigations focused on the order of phase transitions in the ferromagnetic Dicke-Ising chain. The team’s calculations confirm a first-order phase transition to the superradiant phase, a finding that contradicts earlier claims of a second-order transition. This first-order transition is maintained for sufficiently small longitudinal magnetic fields, as verified by both analytical calculations and numerical simulations employing an exact self-consistent approach. Measurements pinpoint a multi-critical point at J ≈ ε/2 = 0. 5, beyond which the order of the transition changes, clarifying the parameter regime where the first-order transition persists. This research delivers a refined understanding of the Dicke-Ising model, resolving discrepancies in previous work and providing a foundation for future investigations into light-matter interactions and quantum phenomena.

Antiferromagnetic Superradiance in the Dicke-Ising Model

This research successfully demonstrates the existence of an intermediate phase exhibiting both antiferromagnetic order and superradiance within the Dicke-Ising model, a feature previously overlooked in other studies. Through quantum Monte Carlo simulations and analysis of the model’s low-energy spectrum, the team confirmed this phase exists and is of limited extent, potentially explaining why it was not observed in earlier work with lower resolution calculations or smaller system sizes. The findings establish that the transition into this intermediate phase is second order, providing a more complete understanding of the model’s quantum phase diagram. Furthermore, the team clarified the nature of phase transitions for ferromagnetic Ising interactions within the Dicke-Ising chain. Contrary to previous claims of a second-order transition to the superradiant phase, this work demonstrates that the transition becomes first order as the longitudinal magnetic field approaches zero, a result supported by Landau theory and a precise self-consistent approach. These findings refine the understanding of quantum phase transitions and provide a more accurate depiction of the Dicke-Ising model’s behaviour.