Many-body localization in large systems

6 problems

• Critical disorder and universality class of the MBL transition

  Open

  If localization does occur above some disorder strength, the transition point and how quantities behave near it are unknown. Small-computer studies disagree with theories built on rare thermal patches.

• Is the random-field Heisenberg chain localized at strong disorder

  Contested

  The standard test case is a chain of quantum spins in random magnetic fields of strength W. The question is whether, for large enough W, an infinitely long chain stays out of equilibrium forever.

• Can a many-body mobility edge exist in the thermodynamic limit

  Contested

  Small-system numerics suggest that at moderate disorder, low-energy states stay localized while high-energy states thermalize, separated by an energy threshold called a mobility edge. Theory argues that hot regions would then wander through the system and thermalize all of it.

• Is quasiperiodic localization stable in two dimensions

  Open

  A non-random but irregular potential, built from waves whose wavelengths have an irrational ratio to the lattice spacing (quasiperiodic), has no rare weak spots, so the rare-region argument may not apply. Whether such systems localize in two dimensions is open.

• Origin of slow relaxation in the intermediate-disorder regime

  Open

  Between the clearly thermal and the apparently localized regimes, disordered chains relax extremely slowly, as power laws in time. What causes this slowness, and whether it ends at a finite time, is unclear.

• Can random disorder localize an interacting system in two dimensions

  Contested

  In two dimensions, rare regions with weak disorder are argued to grow and thermalize their surroundings. Whether that argument holds is not settled.