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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 SciPost Phys. 7, 067 (2019)

Submission summary

As Contributors: Moshe Goldstein
Preprint link: scipost_201908_00003v4
Date accepted: 2019-11-12
Date submitted: 2019-10-30 01:00
Submitted by: Goldstein, Moshe
Submitted to: SciPost Physics
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


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.

Ontology / Topics

See full Ontology or Topics database.

Quantum many-body systems Topological insulators

Published as SciPost Phys. 7, 067 (2019)

Author comments upon resubmission

Dear Editor,
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.

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.

  • validity: high
  • significance: high
  • originality: high
  • clarity: good
  • formatting: good
  • grammar: good

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