Exploring critical states of the quantum Rabi model via Hamiltonian variational ansätze

Abstract: Characterizing quantum critical states towards the thermodynamic limit is essential for understanding phases of matter. The power of quantum simulators for preparing the critical states relies crucially on the structure of quantum circuits and in return provides new insight into the critical states. Here, we explore the critical states of the quantum Rabi model~(QRM) by preparing them variationally with Hamiltonian variational ans\"atze~(HVA), in which the intricated interplay among different quantum fluctuations can be parameterized at different levels. We find that the required circuit depth scales linearly with the effective system size, suggesting that HVA can efficiently capture the behavior of critical states of QRM towards the thermodynamic limit. Moreover, we reveal that HVA gradually squeeze the initial state to the target critical state, with a number of blocks increasing only linearly with the effective system size. Our work suggests variational quantum algorithm as a new probe for the complicated critical states.