Anderson Transitions and Interactions

B. L. Altshuler, A. G. Aronov

Yung‐Chang Cheng, J.W. Chen, Hsueh‐Ju Lin

Nicolas Cherroret, Benoît Vermersch, Jean Claude Garreau +1 more

In disordered systems, our present understanding of the Anderson transition is hampered by the possible presence of interactions between particles. We demonstrate that in boson gases, even weak interactions deeply alter the very nature of the Anderson transition. While there still exists a critical point in the system, below that point a novel phase appears, displaying a new critical exponent, subdiffusive transport, and a breakdown of the one-parameter scaling description of Anderson localization.

An Zhao, Rui-Lin Chu, Shun-Qing Shen

We study the Anderson transition with interactions in one dimension from the perspective of quantum entanglement. Extensive numerical calculations of the entanglement entropy (EE) of the systems are carried out through the density matrix renormalization group algorithm. We demonstrate that the EE can be used for the finite-size scaling (FSS) to characterize the Anderson transition in both noninteracting and interacting systems. From the FSS analysis we can obtain a precise estimate of the critical parameters of the transition. The method can be applied to various one-dimensional models, either interacting or noninteracting, to quantitatively characterize the Anderson transitions.

N. Grewe

Abhishek Singh, W. L. McMillan

The effects of weak, short-ranged interactions on the non-interacting Anderson transition in three dimensions are calculated using a macroscopic renormalisation-group method. The on-site Hubbard (singlet) interaction is found to be relevant at the noninteracting Anderson fixed point; the nearest-neighbour triplet interaction is found to be irrelevant.