From Anderson localization on random regular graphs to many-body localization

Many-body localization phase transition

We use exact diagonalization to explore the many-body localization transition in a random-field spin-1/2 chain. We examine the correlations within each many-body eigenstate, looking at all high-energy states and thus effectively working at infinite temperature. For weak random field the eigenstates are thermal, as expected in this nonlocalized, “ergodic” phase. For strong random field the eigen...

Many-body Localization of Cold

In the seminal 1958 paper, Anderson cites the problem of spin diffusion as a motivation to study the quantum effect of localization [1]. The conclusion about the stability of a localized phase was actually reached there for a single quasiparticle hopping between sites with random, broadly distributed energies. The single-particle localization theory, applicable to various systems comprised of n...

Universalities: from Anderson Localization to Quantum Chaos

Periodic-orbit theory of anderson localization on graphs

We present the first quantum system where Anderson localization is completely described within periodic-orbit theory. The model is a quantum graph analogous to an aperiodic Kronig-Penney model in one dimension. The exact expression for the probability to return to an initially localized state is computed in terms of classical trajectories. It saturates to a finite value due to localization, whi...

Anderson Localization

From the start of their studies students in condensed matter physics are exposed to ordered systems. These systems can be very simple and give insight into the physics of many materials. However it seems that much of what is learned in ordered systems cannot be brought to disordered systems. Instead new conceptual understandings much be reached will very different consquences. One of these is t...