Critical exponents of the two-dimensional quantum contact process
In plain words
In a lattice of Rydberg atoms where an excited atom helps its neighbours become excited and excitations decay, activity either spreads or dies out. Whether quantum coherence changes the universal behaviour of this transition in two dimensions is disputed.
Precise statement
Quantum contact process: Lindblad dynamics with coherent facilitated flips $\Omega \sum_i (\sum_{j\,\mathrm{nn}\,i} n_j) \sigma^{x}_{i}$, decay at rate $\gamma$, and optional classical branching, on a square lattice. Determine the nature of the absorbing-state transition at $\gamma/\Omega$ of order one: directed percolation, tricritical, first order, or a new class. Answer: exponents $\beta, \nu_{\mathrm{perp}}, z$, or a demonstration of first-order behaviour.
What would settle it
Large-scale 2D tensor-network or quantum-jump numerics with finite-size scaling, or Rydberg-array data.
Status in the literature
In 1D, tensor-network work (Carollo et al. 2019) supports directed percolation; mean-field and some 2D studies indicate a first-order transition.