TL;DR
This paper reviews the shift-invert diagonalization method for calculating highly excited states in disordered quantum spin chains exhibiting many-body localization, providing practical guidance, example code, and analysis of computational efficiency.
Contribution
It offers a pedagogical review, practical computational guidance, and example code for shift-invert diagonalization in large disordered spin chains with MBL.
Findings
Eigenstates computed for chains up to size 26
Analysis of simulation parameters for efficient computation
Application of parallel sparse linear algebra techniques
Abstract
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 . 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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