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Dissipation-induced topological insulators: A no-go theorem and a recipe
by Moshe Goldstein
- Published as SciPost Phys. 7, 067 (2019)
|As Contributors:||Moshe Goldstein|
|Date submitted:||2019-10-30 01:00|
|Submitted by:||Goldstein, Moshe|
|Submitted to:||SciPost Physics|
Nonequilibrium conditions are traditionally seen as detrimental to the appearance of quantum-coherent many-body phenomena, and much effort is often devoted to their elimination. Recently this approach has changed: It has been realized that driven-dissipative 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 quantum-correlated steady states, even in the absence of internal Hamiltonian dynamics. An intriguing category of equilibrium many-particle 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 Lindblad-type (Markovian) evolution? Beside its fundamental importance, it may offer novel routes to the realization of topologically-nontrivial 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 no-go theorem stating that a finite-range Lindbladian cannot induce finite-rate exponential decay towards a unique topological pure state above 1D. I construct a recipe for creating such state by exponentially-local dynamics, or a mixed state arbitrarily close to the desired pure one via finite-range dynamics. I also address the cold-atom realization, classification, and detection of these states. Extensions to other types of topological insulators and superconductors are also discussed.
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Published as SciPost Phys. 7, 067 (2019)
Author comments upon resubmission
I would like to thank both Referees for carefully reading the manuscript. I am glad that they both found the work interesting and appropriate for publication in SciPost. Their comments, for which I am thankful and which I have fully implemented, mainly concern the presentation, and helped me in improving it. In the reply to each referee I detail the specific changes made in response to each comment. With this I believe the manuscript is ready for publication.
List of changes
The modifications to the manuscript are detailed in my responses to the Referees.
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 1 on 2019-11-4 (Contributed Report)
In this revised manuscript, the author has addressed appropriately all the points raised in my previous report, and I am now glad to recommend it for publication.
By the way, it would be better to split the newly added Eq. (15) into two lines.