Ferdinand Evers

Hydrodynamics and many-body localization - Numerical transport studies of the spin-1/2 Heisenberg chain

Despite its long history, the spin-1/2 XXZ Heisenberg chain still holds substantial surprises even with respect to very basic fundamental questions. This is true, in particular, for dynamical aspects as they manifest in the spin-spin autocorrelation function. At present, the tools to study this dynamics analytically in a controlled way are missing,  so that much of the current knowledge relies on numerical simulations.

As a first example for a surprise, we discuss the high-temperature behavior at the isotropic point, XXX:  Recent numerical work suggests a critical behavior residing in the KPZ universality class. A fresh numerical study of the corresponding scaling function will be presented that supports this claim.

The second example occurs in the presence of disordered or quasi-periodic magnetic field. For weak disorder a diffusive behavior is expected, while at strong disorder a transition into a many-body localized (MBL) regime has been reported by many authors. Fresh data on the transition will be presented that appear to challenge the Griffith-type scenario, which is considered the prominent paradigm for understanding the MBL-transition up to date.

The talk is based on common work with Felix Weiner (Regensburg), Peter Schmitteckert (Karlsruhe) and Soumya Bera (Mumbai).