Exploring Light-Induced Quantum Criticality and Geometric Frustration in Dicke-Ising Models Using NGSED

Light-matter interactions are fundamental to quantum mechanics, governing phenomena from driven systems in condensed matter physics to the behavior of quantum devices. The analysis of nonclassical correlations between light and matter is crucial for understanding and utilizing quantum effects.

The Dicke model serves as a cornerstone for studying collective light-matter interactions capturing essential features of superradiant phase transition. Expanding upon this framework, the Dicke-Ising and more complex models incorporate additional spin-spin couplings which influence the critical properties of the system.

In this work, we employ the Non-Gaussian State Exact Diagonalization (NGSED) method to analyze the Dicke-Ising models with anti-ferromagnetic screening next-to-nearest neighbour interactions. The NGSED method offers enhanced accuracy in capturing nonclassical correlations through introducing entanglement between spins and gaussian light. We explore how these antiferromagnetic interactions induce geometric frustration within the spin system, affecting its quantum criticality.