Mechanism for Hall conductance of two-band systems against decoherence

System susceptibility and bound-states in structured reservoirs

We propose a formulation to obtain the exact susceptibility for system arbitrary operators to the external fields by means of the whole-system Hamiltonian (system plus reservoir) diagonalization methods, where the dissipative effects directly reflect the nature of the structured non-Markovian reservoir. This treatment does not make the Born-Markovian approximation in structured non-Markovian reservoir. The relations between linear response function and bound-states for the system as well as structured reservoir are found, which shows the photon bound-states and continuous energy spectrum can be readout from the susceptibility, respectively. These results are then used to examine the validity of second-order Born-Markovian approximation, where we find interesting features (e.g., bound-states) are lost in the approximate treatments for open systems. We study the dependence of the response function on the type (spectrum density) of interaction between the system and structured reservoir. We also give the physical reasons behind the disappearance of the bound-states in the approximation method. Finally, these results are also extended to a more general quantum network involving an arbitrary number of coupled-bosonic system without rotating-wave approximation. The presented results might open a new door to understand the linear response and the energy spectrum for non-Markovian open systems with structured reservoirs.

Hall conductance for open two-band system beyond rotating-wave approximation

The response of the open two-band system to external fields would in general be different from that of a strictly isolated one. In this paper, we systematically study the Hall conductance of a two-band model under the influence of its environment by treating the system and its environment on equal footing. In order to clarify some well-established conclusions about the Hall conductance, we do not use the rotating wave approximation (RWA) in obtaining an effective Hamiltonian. Specifically, we first derive the ground state of the whole system (the system plus the environment) beyond the RWA, then calculate an analytical expression for Hall conductance of this open system in the ground state. We apply the expression to two examples, including a magnetic semiconductor with Rashba-type spin-orbit coupling and an electron gas on a square two-dimensional lattice. The calculations show that the transition points of topological phase are robust against the environment. Our results suggest a way to the controlling of the whole system response, which has potential applications for condensed matter physics and quantum statistical mechanics.