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Anderson's localization on the edge of two dimensional time reversal (TR)topological insulator (TI) is studied. For the non-interacting case thetopological protection acts accordingly to the $\mathbb{Z}_2$ classification,leading to conducting and insulating phases for odd and even fillingsrespectively. In the presence of repulsive interaction the phase diagram isnotably changed. We show that for sufficiently strong values of the interactionthe zero temperature fixed point of the TI is conducting, including the case ofeven fillings. We compute the boundaries of the conducting phase for variousfillings and types of disorder.

Interaction Protected Topological Insulators with Time Reversal Symmetry