SciPost Phys. 7, 067 (2019) ·
published 27 November 2019

· pdf
Nonequilibrium conditions are traditionally seen as detrimental to the appearance of quantumcoherent manybody phenomena, and much effort is often devoted to their elimination. Recently this approach has changed: It has been realized that drivendissipative dynamics could be used as a resource. By proper engineering of the reservoirs and their couplings to a system, one may drive the system towards desired quantumcorrelated steady states, even in the absence of internal Hamiltonian dynamics. An intriguing category of equilibrium manyparticle phases are those which are distinguished by topology rather than by symmetry. A natural question thus arises: which of these topological states can be achieved as the result of dissipative Lindbladtype (Markovian) evolution? Beside its fundamental importance, it may offer novel routes to the realization of topologicallynontrivial states in quantum simulators, especially ultracold atomic gases. Here I give a general answer for Gaussian states and quadratic Lindblad evolution, mostly concentrating on 2D Chern insulator states. I prove a nogo theorem stating that a finiterange Lindbladian cannot induce finiterate exponential decay towards a unique topological pure state above 1D. I construct a recipe for creating such state by exponentiallylocal dynamics, or a mixed state arbitrarily close to the desired pure one via finiterange dynamics. I also address the coldatom realization, classification, and detection of these states. Extensions to other types of topological insulators and superconductors are also discussed.
Prof. Goldstein: "I would like to thank the Refe..."
in Report on Dissipationinduced topological insulators: A nogo theorem and a recipe