Contributor info: Dr Francesca Pietracaprina

Francesca Pietracaprina, Fabien Alet

SciPost Phys. 10, 044 (2021) · published 22 February 2021 | Toggle abstract · pdf

We numerically study the possibility of many-body localization transition in a disordered quantum dimer model on the honeycomb lattice. By using the peculiar constraints of this model and state-of-the-art exact diagonalization and time evolution methods, we probe both eigenstates and dynamical properties and conclude on the existence of a localization transition, on the available time and length scales (system sizes of up to N=108 sites). We critically discuss these results and their implications.

Francesca Pietracaprina, Nicolas Macé, David J. Luitz, Fabien Alet

SciPost Phys. 5, 045 (2018) · published 6 November 2018 | Toggle abstract · pdf

We provide a pedagogical review on the calculation of highly excited eigenstates of disordered interacting quantum systems which can undergo a many-body localization (MBL) transition, using shift-invert exact diagonalization. We also provide an example code at https://bitbucket.org/dluitz/sinvert_mbl/. Through a detailed analysis of the simulational parameters of the random field Heisenberg spin chain, we provide a practical guide on how to perform efficient computations. We present data for mid-spectrum eigenstates of spin chains of sizes up to $L=26$. This work is also geared towards readers with interest in efficiency of parallel sparse linear algebra techniques that will find a challenging application in the MBL problem.