Dissipation-induced topological insulators: A no-go theorem and a recipe

TL;DR

This paper investigates the possibility of creating topological insulator states through dissipative dynamics, proving limitations with finite-range Lindbladians and proposing methods to achieve desired states in quantum systems.

Contribution

It establishes a no-go theorem for finite-range Lindbladians to generate pure topological states and offers a recipe for approximating such states using exponentially-local dynamics.

Findings

Finite-range Lindbladians cannot produce pure topological states in more than 1D.

A method is proposed to approximate topological states with finite-range dynamics.

Implications for cold-atom experiments and topological quantum simulation are discussed.

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 the example of 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.