Diffusive dynamics of fractionalized particles and the enhanced conductivity at the border of the neutral-ionic transition

We study the diffusive dynamics of the classical one-dimensional lattice model of mobile particles featuring the incoherent metallic state of the organic TTF-CA found in the vicinity of the neutral-ionic(NI) transition. The particles are strongly correlated and feel the alternating site potentials, exhibiting uniform ionic (I) Mott insulating and neutral band insulating (N) phases when the Coulomb interaction and site potentials are large, respectively. We focus on the neutral-ionic domain walls (NIDW) activated by their competition, which are typically regarded as fractionalized particles. The finite temperature phase diagram reveals a thermodynamically stable NIDW phase not found in previous literature that emerges at the triple point, where the transition line splits into two first-order lines toward the critical endpoints. We analyze the long-time behavior of dynamics of the NIDWs and find that it captures the diffusive transport of the system. The conductivity derived from the diffusion constant and the number population of NIDWs shows a strong enhancement inside the NIDW phase, which can explain the large conductivity at the NI crossover found in TTF-CA.