Quantum Phase Transitions in Electronic Systems We have developed a numerical method to study quantum phase transition in various two dimensional strongly correlated electron systems. We present a phase diagram for a double quantum well bilayer electron gas in the quantum Hall regime at total filling factor v = 1, based on exact numerical calculations of the topological Chern number matrix and the (inter-layer) superfluid density. We find three phases: a quantized IIall state with pseudo-spin superfluidity, a quantized IIall state with pseudo-spin "gauge-glass" order, and a decoupled composite Fermi liquid. Comparison with experiments provides a consistent explanation of the observed quantum Hall plateau, Hall drag plateau and vanishing Hall drag resistance, as well as the zero-bias conductance peak effect, and suggests some interesting points to pursue experimentally.
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