Field Theory Approach to Many-Body Localization

We introduce an analytic approach to many-body localization (MBL) in random spin chains. We consider MBL within a first quantized framework where it becomes a localization phenomenon in the high-dimensional lattice defined by the Hilbert space of the clean system. Designed in analogy with the field-theory description of single particle localization, our approach describes wave package propagation on that lattice after a disorder average has been performed and the system is controlled by only a few universal parameters. We discuss the stability of an ergodic weak disorder and a localized strong disorder phase, respectively, and demonstrate that the latter is protected by mechanisms which put MBL outside the universality class of Anderson localization.

Figure 1

The coupling of modes $T_d$ diagonal in Hilbert space (dark shaded) to weakly off-diagonal modes, $T_v$ (light shaded). Lines indicated by $+/-$ denote particle-hole amplitudes stationary at sites $n$ or $m$, and the dots interaction vertices.