Topology by dissipation: Novel transport properties and disorder-induced criticality

Nonequilibrium conditions are traditionally seen as detrimental to the appearance of quantum coherent many-body phenomena in condensed matter systems, and much effort is often devoted to their elimination. Recently this approach has changed: It has been realized that driven-dissipative Markovian dynamics of the Lindblad type could be used as a resource. By proper engineering of the reservoirs and their local 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 nontrivial equilibrium many-particle phases are those which are distinguished by topology rather than by symmetry. Natural questions thus arise: Which of these topological states can be achieved as the result of purely dissipative Lindblad-type dynamics? Could they display novel behavior, with no equilibrium analogues? Besides the fundamental importance of these issues, they may offer novel routes to the realization of topologically-nontrivial states in quantum simulators, especially ultracold atomic gases.

In our previous work we have provided a no-go theorem determining which Gaussian (noninteracting) topological states are achievable as the unique steady states of local dissipative dynamics, as well as a general recipe for creating, identifying and classifying the achievable states in ultracold atoms and related systems. After reviewing this work I will discuss two newer developments:

1. What are the resulting transport properties, such as persistent currents and conductivity? We find that, in contrast with equilibrium systems, the usual relation between the Chern topological number and the Hall conductivity is broken. We explore the intriguing edge dynamics and elucidate under which conditions the Hall conductivity is quantized.

2. We show that dissipation-induced topology is robust against weak disorder, but may break down under strong enough disorder, with a critical point separating the two regimes. Surprisingly, disordered dissipation leads to a critical point similar to the equilibrium one, while disordered Hamiltonian in the presence of dissipation leads to a novel critical point with significantly different critical exponents.