Abstract:
We theoretically study single and multi particle dynamics on long-range hopping one di-
mensional fermionic and bosonic lattice systems with hopping decaying as a power-law with exponent µ. The lattice is further subjected to local particle number conserving dephasing at each of its sites. In the limit of strong dephasing, we adiabatically eliminate the coherences and obtain effective dynamical equations for the two-point and four-point correlation functions in the site basis. We devise a novel bond length representation for the four-point correlator, which holds for the alternating initial state and allows us to numerically simulate four-point correlator dynamics for significantly large system sizes. For single particle dynamics, we find that even moments of the density profile of a single exciton shows one-parameter scaling behaviour in the form of Family-Viscek (FV) scaling for µ >1.5 with diffusive scaling exponents, whilst for µ < 1.5 the moments fail to show FV scaling. For multi particle dynamics, we find that observables such as particle transport and particle number fluctuations show FV scaling with diffusive scaling exponents for µ >1.5 and super-diffusive scaling exponents for µ<1.5. We further use the bond length representation to analytically derive the exact FV scaling exponents for particle number fluctuation on fermionic tight-binding lattice.
