Exact solution of the facilitated totally asymmetric simple exclusion process

We obtain the exact solution of the facilitated totally asymmetric simple exclusion process (F-TASEP) in 1D. The model is closely related to the conserved lattice gas (CLG) model and to some cellular automaton traffic models. In the F-TASEP a particle at site j in Z jumps, at integer times, to site j + 1, provided site j - 1 is occupied and site j + 1 is empty. When started with a Bernoulli product measure at density ρ, the system approaches a stationary state. This non-equilibrium steady state (NESS) has phase transitions at ρ = 1/2 and ρ = 2/3. The different density regimes 0 <ρ < 1/2, 1/2 <ρ < 2/3, and 2/3 <ρ < 1 exhibit many surprising properties; for example, the pair correlation g(j) = <η(i) η (i + j)> satisfies, for all n ∈ Z, Σ^k(n+1) _j=kn+1 g(j) = kρ², with k = 2 when 0 ≤ ρ ≤ 1/2, k = 6 when 1/2 ≤ ρ ≤ 2/3, and k = 3 when 2/3 ≤ ρ ≤ 1. The quantity lim_L→∞ V_L/L, where V_L is the variance in the number of particles in an interval of length L, jumps discontinuously from ρ (1 - ρ) to 0 when ρ → 1/2 and when ρ → 2/3.