Robustness of complex many-body networks: Novel perspective in 2D metal-insulator transition

We present a novel theoretical framework established by complex network analysis for understanding the phase transition beyond the Landau symmetry breaking paradigm. In this paper we take a two-dimensional metal-insulator transition driven by electron correlations for example. Passing through the transition point, we find a hidden symmetry broken in the network space, which is invisible in real space. This symmetry is nothing but a kind of robustness of the network to random failures. We then show that a network quantity, small-worldness, is capable of identifying the phase transition with/without any symmetry breaking in the real space and behaving as a new order parameter in the network space. We demonstrate that whether or not the symmetry is broken in real space a variety of phase transitions in condensed matters can be characterized by the hidden symmetry breaking in the weighted network, that is to say, a decline in network robustness.