Localization Parameters for Two Interacting Particles in Disordered Two-Dimensional Finite Lattices

Abstract

I study spreading of two interacting hardcore bosons in disordered two-dimensional finite lattices from an initial occupation of two adjacent sites. The parameters related to the spreading of the particles provide an insight on the effect of interaction. I find that the presence of interaction makes the particles less localized than the non-interacting ones within the range of disorder strength W ≤ 4 and interaction strength V ≤ 4 . If the interaction strength is higher, then particles localize more. A transition with changes in the character of dominant correlations is found at critical disorder strengths for each chosen strength of interaction. The nature of correlations between the particles as nearest neighbours becomes dominant beyond these disorder strengths.

Mobility edge of two interacting particles in three-dimensional random potentials

“…While several numerical studies [31][32][33][34][35][36][37][38] have confirmed the claim for one-dimensional systems, the situation is much less clear in higher dimensions, where the computational cost limits the system sizes that can be explored. In particular an Anderson transition was predicted 39,40 to occur in two dimensions (see also 41 for a recent study of the two-particle dynamics in a similar model).…”

Scaling theory of few-particle delocalization

“…The main difficulty with the scaling theory presented here is the limited power of exact numerical solutions, which are at its heart. New numerical results for larger system sizes might provide new insights, exemplified by the recent controversy over whether n = 2 particle states in d = 2 can delocalize [29,30]. Note that these new results do not necessarily contradict the possibility of a delocalization transition, because it was shown that for large disorder there is no transition as a function of interaction strength, whereas Refs.…”

“…Surprisingly, however, is that in d = 2 dimensions an exact calculation of the two-particle Green's function showed a delocalization transition [26][27][28]. Recent results claim the opposite [29,30], but without showing scaling as a function of disorder strength. Three-particle states have been discussed using perturbation theory [23,31] and an increased localization length was observed for relatively large disorder [24].…”

Spectral density of interacting pairs in low-dimensional finite lattices

“…A brief description is given in the method section for the reader. With Berciu's method, the Green's functions can be computed efficiently for the cases of zero and non-zero external magnetic fields as well as for disordered systems [29]. The bound pairs can be found in general graph architectures where the quantum transport may prove relevant to quantum technologies.…”