Localization-delocalization transition at weak coupling in two-color matrix QCD

We numerically investigate the matrix model of two-color one-flavor adjoint QCD (matrix- QCD 2 , 1 adj ) in the weak coupling regime (small g ) and in the chiral limit. The Yang-Mills potential has two distinct gauge invariant minima: one at A i = 0 and the other at A i = σ i 2 g . We show that when the chiral chemical potential c ≤ 3 2 there is a quantum phase transition (QPT) at g 0 * ≃ 0.143 : for g < g 0 * , the ground-state wave function is localized near A i = 0 , while for g > g 0 * , the ground state is delocalized over the gauge configuration space. The transition between these two phases is singular, with the ground state at g 0 * being distinctly different from that of g 0 * ± | ε | . At g 0 * , we show that the square of the chromoelectric field vanishes, strongly suggesting that the system is in a “dual superconductor” phase. Numerical evidence shows that the localization-delocalization phenomenon holds for the first and second excited states as well, leading us to conjecture that there are an infinite number of isolated singular points g 0 * > g 1 * > g 2 * > ⋯ accumulating to g = 0 . For c = 1 , the model formally possesses N = 1 supersymmetry. We show that in the localized phase (i.e., for g < g 0 * ) the supermultiplet structure is disrupted and supersymmetry is spontaneously broken.