The quantum phase transitions of dimer chain driven by an imaginary ac field

A topologically equivalent tight binding model is proposed to study the quantum phase transitions of dimer chain driven by an imaginary ac field. I demonstrate how the partner Hamiltonian is constructed by a similarity transformation to fulfil the $mathcal{PT}$ symmetry. The $mathcal{PT}$ symmetry of the partner model allows us to study the topological properties of the original non-Hermitian model as the Bloch bands of the Hermitian system. The quantum phase transitions are discussed in different frequency regime. The approach has the potential applications to investigate the topological states of matter driven by the complex external parameters.