Shift-invert diagonalization of large many-body localizing spin chains

Francesca Pietracaprina (1, 2) , Nicolas Macé (1, 2) , David J. Luitz (3, 4) , Fabien Alet (1, 2)

1 FFC - Fermions Fortement Corrélés (LPT)
2 LPT - Laboratoire de Physique Théorique
3 TUM - Technische Universität Munchen - Technical University Munich - Université Technique de Munich
4 MPI-PKS - Max-Planck-Institut für Physik komplexer Systeme

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.

Domaines: Physique Numérique [physics.comp-ph]; Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]

Francesca Pietracaprina, Nicolas Macé, David J. Luitz, Fabien Alet. Shift-invert diagonalization of large many-body localizing spin chains. SciPost Physics, 2018, 5 (5), pp.045. ⟨10.21468/SciPostPhys.5.5.045⟩. ⟨hal-01913091⟩