Speaker
Description
The field of cavity qed materials seeks to modify the properties of bulk materials by coupling them to an electromagnetic cavity at equilibrium. When the material is, e.g., composed of magnetic dipoles, the resulting system is described by a generalized Dicke model. Under certain conditions, the cavity modes can be traced out, leaving a spin Hamiltonian with cavity-mediated (effective) spin-spin interactions [1]. Here, we leverage this result to study the relationship between the effective spin model and the underlying Dicke model. We reverse the mapping and use it as a generalized Hubbard–Stratonovich transformation. We show that long-range quantum models can be mapped exactly to generalized Dicke models and use this result to provide an analytical solution in the thermodynamic limit. We illustrate the method on the Ising chain in transverse field. The critical behaviour is found to be universal for all strong long-range models and lattice dimensionalities, in agreement with previous numerical results [2]. The expression for the order parameter is equivalent to the one provided by mean-field theory, proving the exactness of the later. Finally, we study the algebraic decay of correlations and characterize its dependence on the range of interactions in the full phase diagram.
References:
[1] J. Román-Roche and D. Zueco, SciPost Phys. Lect. Notes, 50 (2022).
[2] E. Gonzalez Lazo, M. Heyl, M. Dalmonte and A. Angelone, SciPost Phys. 11, 076 (2021).
