Orthogonality Catastrophe and Spontaneous Symmetry Breaking in Double-layer Fermi-liquid-like States

The double-layer electron system with total filling factor $\nu=1/2$ can be regarded as two separate Fermi-liquid-like states with $\nu=1/4$ when the layer separation is sufficiently large and there is no tunneling. The weak tunneling in this state suffers an orthogonality catastrophe and it becomes irrelevant. Using the symmetric and antisymmetric combinations of layer indices as the pseudospin degrees of freedom, we show that there exists the first order transition from the above pseudospin unpolarized state to the pseudospin polarized Fermi-liquid-like state with $\nu=1/2$ as the tunneling strength becomes sufficiently large.