Many-Body Delocalization as Symmetry Breaking

We present a framework in which the transition between many-body localized (MBL) phase and an ergodic one is symmetry breaking. consider random Floquet spin chains, expressing their averaged spectral form factor (SFF) as function of time terms transfer matrix that acts space direction. The SFF determined by leading eigenvalues this matrix. In MBL phase, eigenvalue unique, symmetry-unbroken while at late times are asymptotically degenerate, system with degenerate symmetry-breaking phases. identify broken matrix, introduce local order parameter for transition, show associated correlation functions long-ranged only phase.