Shift-invert diagonalization of large many-body localizing spin chains
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/sinver...
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| Format: | Article |
| Language: | English |
| Published: |
SciPost
2018-11-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.5.5.045 |
| Summary: | 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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| ISSN: | 2542-4653 |