Interacting particles at a metal-insulator transition

Abstract

We study the influence of many-particle interaction in a system which, in the single particle case, exhibits a metal-insulator transition induced by a finite amount of onsite pontential fluctuations. Thereby, we consider the problem of interacting particles in the one-dimensional quasiperiodic Aubry-André chain. We employ the density-matrix renormalization scheme to investigate the finite particle density situation. In the case of incommensurate densities, the expected transition from the single-particle analysis is reproduced. Generally speaking, interaction does not alter the incommensurate transition. For commensurate densities, we map out the entire phase diagram and find that the transition into a metallic state occurs for attractive interactions and infinite small fluctuations -in contrast to the case of incommensurate densities. Our results for commensurate densities also show agreement with a recent analytic renormalization group approach. 71.30.+h,71.27.+a

Stability of the superfluid state in a disordered one-dimensional ultracold fermionic gas

“…The numerical results of [15] indicate that the critical disorder at which the metal-insulator transition occurs depends on the strength of the interaction. By contrast the DMRG analysis of [16] concluded that, for spinless fermions, the critical disorder is the same as in the noninteracting case. In [19], also employing a DMRG technique, it was found that the presence of a weak disordered potential enhances superfluidity.…”

“…More specifically we determine numerically the location of the critical disorder λ ins c at which the metal-insulator transition occurs. Different quantities, such as density fluctuations [26] or the conductance [16], provide a similar estimation of localization effects. However the numerical value of λ ins c might depend weakly on the observable employed [27].…”

Disorder and interactions in one-dimensional systems

“…The authors believe the earlier attempt 19 based on an RG procedure overestimates the delocalized regime by a factor of 4. Other authors, Römer 24 and Schuster et al, 25 have mapped out an extended regime for the same model but with the Aubry-André quasiperiodic potential. However, its shape in disorder-interaction phase space takes on a different form.…”

Dense gaps in the interacting Aubry-André model

“…Given the complexity of the single particle problem, and the critical behavior produced by the many body interaction on free particles, it is not surprising that quantitative predictions for the interacting Aubry-André model are a difficult task, and have been pursued mostly by numerical methods in the fermionic [14], [15], [16], [17] and bosonic case [18], [19], [20]; non perturbative effects could however be missed due to size limitations. On the analytical side, in [21] it was studied a system of interacting fermions subject to a weak quasi-periodic potential with exponentially fast decaying harmonics, and insulating behavior was rigorously proved for chemical potentials in the gaps, provided that the corresponding harmonic is non vanishing; for Aubry-André potential, this says that the largest gap persists.…”