Quantum Simulation of Quantum Berezinskii-Kosterlitz-Thouless Transition for Interacting Light-Matter System: A Few Exact Results

An attempt is made to understand the quantum simulation of quantum Berezinskii-Kosterlitz-Thouless (QBKT) transition for interacting light-matter system. We derive the QBKT equation for our system along with the exact results. We present emergence of different quantum phases in the different regimes of parameter space for this quantum simulated system. We interpret the collective excitations of the system in terms of bosonic excitations (Bose metal phase) as well as the photon blocked state (photonic insulator state) in our study. We present the behavior of renormalization group (RG) flow lines from the numerical studies of RG flow equations and also from the exact solution. We study the quantum critical surface of the simulated model Hamiltonian and also present the exact results for Majumdar-Ghosh point as well as for refermionization point from the perspective of quantum simulation.