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Dissipation-induced topological insulators: A no-go theorem and a recipe
by Moshe Goldstein
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Moshe Goldstein |
| Submission information | |
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| Preprint Link: | scipost_201908_00003v4 (pdf) |
| Date accepted: | Nov. 12, 2019 |
| Date submitted: | Oct. 30, 2019, 1 a.m. |
| Submitted by: | Goldstein, Moshe |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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.
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.
Sincerely yours,
Moshe Goldstein
List of changes
The modifications to the manuscript are detailed in my responses to the Referees.
Published as SciPost Phys. 7, 067 (2019)
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By the way, it would be better to split the newly added Eq. (15) into two lines.