Quantum response theory for open systems and its application to Hall conductance

TL;DR

This paper develops a quantum nonlinear response theory for open systems, enabling the calculation of Hall conductance at finite temperature and revealing the robustness of topological phase transition points despite environmental effects.

Contribution

It introduces a quantum nonlinear response framework for open systems and applies it to derive and analyze Hall conductance in various models.

Findings

Hall conductance remains stable at topological transition points despite environmental interactions

The theory accurately describes response up to second order in perturbation for open systems

Application to two-band and lattice models demonstrates practical utility

Abstract

Quantum linear response theory considers only the response of a closed quantum system to a perturbation up to first order in the perturbation. This theory breaks down when the system subjects to environments and the response up to second order in perturbation is not negligible. In this paper, we develop a quantum nonlinear response theory for open systems. We first formulate this theory in terms of general susceptibility, then apply it to deriving the Hall conductance for the open system at finite temperature. Taking the two-band model as an example, we derive the Hall conductance for the two-band model. We calculate the Hall conductance for a two-dimensional ferromagnetic electron gas and a two-dimensional lattice model via different expressions for $d_{\alpha}(\vec p), \ \alpha=x,y,z$. The results show that the transition points of topological phase almost remain unchanged in the presence of environments.