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.
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- 1 Université de Toulouse / University of Toulouse
- 2 Max-Planck-Institut für Physik komplexer Systeme / Max Planck Institute for the Physics of Complex Systems
- 3 Technische Universität München / Technical University of Munich [TUM]
- Agence Nationale de la Recherche [ANR]
- Horizon 2020 (through Organization: European Commission [EC])
- Partnership for Advanced Computing in Europe AISBL (PRACE) (through Organization: Partnership for Advanced Computing in Europe [PRACE])