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We study many-body localization (MBL) transition in disordered Kicked Ising model using a polynomially filtered exact diagonalization (POLFED) algorithm. We quantitatively demonstrate that finite size effects at the MBL transition in disordered Kicked Ising model are less severe than in random field XXZ spin chains widely studied in the context of MBL. This allows us to observe consistent signatures of the transition to MBL phase for a several indicators of ergodicity breaking. We show that an assumption a power-law divergence of the correlation length at the MBL transition yields a critical exponent ν ≈ 2, consistent with the Harris criterion for 1D disordered systems.
The datasets described below were used to produce all figures in the linked arXiv paper.
Figure 1. The ergodic-MBL crossover in Kicked-Ising Model. Jupyter notebook creating plots of Fig. 1 is fig1.ipynb; it employs data stored in directory ./fig1/
Figure 2. Finite size scaling analysis of ergodic-MBL crossover in Kicked Ising Model. Jupyter notebook creating plots of Fig. 2 is fig2.ipynb; it employs data stored in directory ./fig2/
Figure S3. The average gap ratio and the rescaled entanglement entropy as functions of disorder strength W for Kicked Ising model. Jupyter notebook creating plots of Fig. S3 is figS3.ipynb; it employs data stored in directory ./figS3/
Figure S4. The average quantum mutual information in Kicked Ising Model. Jupyter notebook creating plots of Fig. S4 is figS4.ipynb; it employs data stored in directory ./figS4/
Figure S5. The average Schmidt gap and spin stiffness as functions of disorder strength W in Kicked Ising Model. Jupyter notebook creating plots of Fig. S5 is figS5.ipynb; it employs data stored in directory ./figS5/
Figure S6. 6. The disorder strength WT for various choices of the threshold pX compared with the crossing point. Jupyter notebook creating plots of Fig. S6 is figS6.ipynb; it employs data stored in directory ./figS6/
Figure S7. Supplementary data for finite size scaling analysis of ergodic-MBL crossover in Kicked Ising Model. Jupyter notebook creating plots of Fig. S7 is figS7.ipynb; it employs data sets stored in directory ./figS7/
[Parent Directory]| fig1 | DIR | |
| fig2 | DIR | |
| figS3 | DIR | |
| figS4 | DIR | |
| figS5 | DIR | |
| figS6 | DIR | |
| figS7 | DIR | |
| fig1.ipynb | 196kB | |
| fig2.ipynb | 140kB | |
| figS3.ipynb | 148kB | |
| figS4.ipynb | 109kB | |
| figS5.ipynb | 205kB | |
| figS6.ipynb | 67kB | |
| figS7.ipynb | 103kB |
