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

• DOI: 10.21468/scipostphys.5.5.045
• Publication Date: 2018-11-06T02:17:27Z
• Authors: Francesca Pietrac...; Nicolas Macé; David J. Luitz; Fabien Alet
• Keywords: Code (set theory)

We provide a pedagogical review on the calculation of highly excited eigenstates disordered interacting quantum systems which can undergo many-body localization (MBL) transition, using shift-invert exact diagonalization. also an example code at https://bitbucket.org/dluitz/sinvert_mbl. Through detailed analysis simulational parameters random field Heisenberg spin chain, we practical guide how to perform efficient computations. present data for mid-spectrum chains sizes up L=26 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>L</mml:mi><mml:mo>=</mml:mo><mml:mn>26</mml:mn></mml:mrow></mml:math> . This work is geared towards readers with interest in efficiency parallel sparse linear algebra techniques that will find challenging application MBL problem.