General response formula and application to topological insulator in quantum open system

H. Z. Shen, M. Qin, X. Q. Shao, and X. X. Yi
Phys. Rev. E 92, 052122 – Published 17 November 2015

Abstract

It is well-known that the quantum linear response theory is based on the first-order perturbation theory for a system in thermal equilibrium. Hence, this theory breaks down when the system is in a steady state far from thermal equilibrium and the response up to higher order in perturbation is not negligible. In this paper, we develop a nonlinear response theory for such quantum open system. We first formulate this theory in terms of general susceptibility, after which we apply it to the derivation of Hall conductance for open system at finite temperature. As an example, the Hall conductance of the two-band model is derived. Then we calculate the Hall conductance for a two-dimensional ferromagnetic electron gas and a two-dimensional lattice model. The calculations show that the transition points of topological phase are robust against the environment. Our results provide a promising platform for the coherent manipulation of the nonlinear response in quantum open system, which has potential applications for quantum information processing and statistical physics.

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  • Received 30 June 2015
  • Revised 12 October 2015

DOI:https://doi.org/10.1103/PhysRevE.92.052122

©2015 American Physical Society

Authors & Affiliations

H. Z. Shen1,2, M. Qin1,2, X. Q. Shao1, and X. X. Yi1,*

  • 1Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China
  • 2School of Physics and Optoelectronic Technology Dalian University of Technology, Dalian 116024, China

  • *yixx@nenu.edu.cn

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Vol. 92, Iss. 5 — November 2015

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