Dissipative phase transitions of the Dicke-Ising model

TL;DR

This work analyzes nonequilibrium phase transitions in the Dicke-Ising model (DIM) under Markovian dissipation using a mean-field framework supplemented by stability analysis. It contrasts the transverse and longitudinal DIM, showing that dissipation preserves the transverse phase structure with modest shifts, but induces a bistable, first-order transition regime in the longitudinal DIM, including a tetracritical point. The results reveal how dissipation, light–matter coupling, and spin interactions jointly shape steady states and phase boundaries, offering a theoretical route to controllable nonequilibrium states in solid-state quantum simulators. The findings provide a foundation for exploring open quantum many-body physics in realistic settings and suggest robustness of the observed phenomena beyond mean-field.

Abstract

The dissipative phase transitions in the open transverse and longitudinal Dicke-Ising model (DIM), which incorporates nearest-neighbor Ising-type spin interactions into the Dicke framework, are investigated within a mean-field approach and further validated by detailed stability analysis. While the dissipative phase diagram of the transverse DIM is only slightly shifted upward compared with its ground-state counterpart, dissipation in the longitudinal DIM stabilizes bistable nonequilibrium steady states and induces first-order phase transitions that are absent in the ground-state phase diagram. This bistable phase is characterized by the coexistence of superradiant and antiferromagnetic orders, and it converts a ground-state triple point into a tetracritical point, at which the boundaries of the first- and second-order transitions intersect. Our results reveal that the interplay among spin interactions, light-matter coupling, and dissipation supports a diverse set of nonequilibrium phase transitions and provides broad tunability of the phase diagram. These findings offer a theoretical foundation for exploring nonequilibrium physics in realistic open solid-state quantum systems.

Figures (3)

• Figure 1: (a-b) Steady-state phase diagrams of the dissipative DIM in the $J$-$g$ plane with fixed $\Omega = \omega$ for the transverse DIM (a) and longitudinal DIM (b). The phases are labeled as PN (blue), AFN (green), PS (orange), AFS (red), and PS+AFN (purple). Solid blue, red, and black lines mark the boundaries of second-order transitions, while dashed blue and red lines indicate the first-order transition boundaries. The tetracritical point is highlighted by a red circle. The dissipative strength is fixed at $\kappa = 0.5\omega$. (c,d) Corresponding ground-state phase diagrams for (a,b). The black dashed line $g_{c0}^{x,\mathrm{GS}}$ indicates a first-order transition separating the AFN and PS phases. The red square represents the tricritical point.
• Figure 2: Order parameters $m_{\mathrm{AF}}^z$ and $n$ as functions of the coupling strength $g$ in the dissipative transverse DIM with $J = 0.3\omega$. The blue and red solid lines correspond to $m_{\mathrm{AF}}^z$ and $n$, respectively. The dissipation rate is fixed at $\kappa = 0.5\omega$.
• Figure 3: Order parameters as functions of the coupling strength $g$ at $J = 0.3\omega$ for open longitudinal DIM with $\kappa = 0.5\omega$ (a), and the corresponding closed system with $\kappa = 0$ (b). Blue lines represent the staggered magnetization along the $x$ direction, $m_{\mathrm{AF}}^x$, while red lines represent the mean photon number $n$. Circular markers correspond to values obtained in the AFN phase, whereas triangular markers indicate results in the PS phase.