Universality class of the one-dimensional quantum contact process

Determine the character and universality class of the absorbing-state phase transition in the one-dimensional quantum contact process in which an excitation on site j can be created only if exactly one neighboring site is already excited (the QXP model), under homogeneous coherent excitation rate λ and spontaneous decay from the excited to the ground state at rate γ; specifically, establish whether this transition belongs to the directed percolation universality class or a different universality class and characterize its critical behavior.

Background

Quantum contact processes with spontaneous decay exhibit absorbing-state phase transitions whose universality class depends on spatial dimension. For dimensions d ≥ 2, prior studies indicate second-order transitions in the directed percolation (DP) universality class.

For the one-dimensional case of the kinetically constrained quantum contact process considered here (the QXP model, where excitations can only be created in the presence of exactly one excited neighbor), the nature of the absorbing-state transition remains unresolved. Clarifying whether the transition is DP or belongs to a different universality class, and determining its critical properties, is an explicit open problem highlighted in the introduction.

References

It has been shown that adding spontaneous decay at rate $\gamma$ from the excited to the ground state, and assuming homogeneous excitation rates, also this (quantum) model shows an absorbing-state phase transition at some critical value of $\lambda/\gamma$ depending on the spatial dimension . Although in dimensions $d=2$ and higher the transition is believed to be of second order and of DP universality, the character of the transition in $d=1$ remains not fully understood, but is likely not of the DP universality class .

— Quantum Contact Processes on a Topological Lattice  (2604.03184 - Bohm et al., 3 Apr 2026) in Introduction, Page 1