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Title: Can local dissipation prepare a pure chiral topological state?
Plain: Engineered loss can pump atoms into a chosen state, like water settling at the bottom of a bowl. It is unknown whether this works for states with a built-in handedness, such as the quantum Hall states, using only short-range processes.
Precise: Fermions or spins on a 2D lattice evolving under a Lindblad master equation with finite-range jump operators and finite-range Hamiltonian. Determine whether a pure state with nonzero Chern number (or nonzero Hall conductance) can be the unique steady state with a Liouvillian gap that stays finite as $N \to \infty$. Known obstructions: quadratic (Gaussian) local Lindbladians cannot do it (Budich, Zoller, Diehl, PRA 2015), and local commuting-projector Hamiltonians have zero Hall conductance (Kapustin, Fidkowski, CMP 2019). Answer: a general no-go proof covering interacting Lindbladians, or an explicit local Lindbladian that works.
Settled by: A theorem extending the Gaussian obstruction to interacting finite-range Lindbladians, or a constructed counterexample with a proven size-independent Liouvillian gap.
Kind: well-posed
Answer type: proof
References: (empty)
Literature status: open
Status note: Approximate dissipative schemes for Chern and fractional Chern insulators exist (Liu, Bergholtz, Budich, Phys. Rev. Research 2021), but none gives an exact pure chiral steady state with a finite gap.
Posed since: 2015