Abstract We review our recent results on Anderson localization in systems of two interacting particles coupled by contact interactions. Based on an exact mapping to an effective single-particle problem, we numerically investigate the occurrence of metal-insulator phase transitions for the pair in two-(2D) and three-dimensional (3D) disordered lattices. In two dimensions, we find that interactions cause an exponential enhancement of the pair localization length with respect to its single-particle counterpart, but do not induce a delocalization transition. In particular we show that previous claims of 2D interaction-induced Anderson transitions are the results of strong finite-size effects. In three dimensions we find that the pair undergoes a metal-insulator transition belonging to the same (orthogonal) universality class of the noninteracting model. We then explore the phase diagram in the space of energy E, disorder W and interaction strength U, which reveals a rich and counterintuitive structure, endowed with multiple metallic and insulating phases. We point out that this phenomenon originates from the molecular and scattering-like nature of the pair states available at given energy and disorder strength.
We analyze the unanalytical structure of metal-insulator transition (MIT) in infinite dimensions. A multiple-valued structure in Green's function and other thermodynamical quantities with respect to the interaction strength U are observed at low temperatures by introducing a transformation into the dynamical mean-field equation of Hubbard model. A complete description of stable, metastable, and unstable phases is established in the regime
Uc1(T)<U<Uc2(T). The Maxwell construction is performed to evaluate the MIT line
U∗(T). We show how the first-order MIT at
U∗(T) for
T>0 evolves into the second-order one at
Uc2(0) for
T=0. The phase diagram near MIT is presented.