Quantum metric tensor of the Dicke model: Analytical and numerical study

We compute both analytically and numerically the quantum metric tensor and its scalar curvature for the Dicke model. In the analytical setting we consider the thermodynamic limit and carry out the computations by means of the truncated Holstein-Primakoff approximation. We also study the exactly solvable case ω0=0 and find that the corresponding non-Abelian QMT effectively reduces to just one metric tensor with zero determinant. In the numerical case we use an efficient basis to diagonalize the Hamiltonian for four different system's sizes. For the components of the quantum metric tensor and their derivatives, we find a remarkable agreement between the numerical and analytical results, with the metric's peaks signaling the precursors of the quantum phase transition. In the case of the scalar curvature, there are some differences between the numerical and analytical results that can be traced back to the behavior of the combination of the metric components' derivatives. Notably, the scalar curvature in the thermodynamic limit is continuous across the quantum phase transition and, in that zone, it approximately matches the numerical results.