This file FILENAME was updated on 2020-11-16 ------------------- GENERAL INFORMATION ------------------- Title of Dataset: Supporting Data for Spectral rigidity of non-Hermitian symmetric random matrices near the Anderson transition Author Information: Principal Investigator Contact Information Name: Boris I. Shklovskii Institution: University of Minnesota Address: School of Physics and Astronomy, 116 Church Street S.E., Minneapolis, Minnesota 55455 Email: shklo001@umn.edu ORCID: Associate or Co-investigator Contact information Name: Yi Huang Institution: University of Minnesota Address: School of Physics and Astronomy, 116 Church Street S.E., Minneapolis, Minnesota 55455 Email: huan1756@umn.edu ORCID: https://orcid.org/0000-0001-5702-0705 Date of data collection: 20200601 - 20200701 Geographic location of data collection: University of Minnesota Information about funding sources that supported the collection of the data: This research was supported by a grant from the National Science Foundation through MRSEC award DMR-1420013. -------------------------- SHARING/ACCESS INFORMATION -------------------------- 1. Licenses/restrictions placed on the data: CC01 2. Links to publications that cite or use the data: Huang, Yi; Shklovskii, B. Spectral Rigidity of Non-Hermitian Symmetric Random Matrices Near the Anderson Transition. Physical review. B 2020, 102 (6). https://doi.org/10.1103/PhysRevB.102.064212. 3. Links to other publicly accessible locations of the data: 4. Links/relationships to ancillary data sets: 5. Was data derived from another source? 6. Recommended citation for the data: Shklovskii, Boris, I; Huang, Yi. (2020). Supporting Data for Spectral rigidity of non-Hermitian symmetric random matrices near the Anderson transition. Retrieved from the Data Repository for the University of Minnesota, https://doi.org/10.13020/5rj1-zz56. --------------------- DATA & FILE OVERVIEW --------------------- 1. File List A. Filename: data Short description: The set of data required to produce the plot of number variance of eigenvalues inside disks in the complex plane. The data files are in format .dat, which should be opened by MatLab. MatLab 2019 was used to manipulate the data. The files are named by several parameters: d = dimensionality of the lattice L = size of each side of the lattice W = disorder parameter. Each column in the file represents the number of eigenvalues inside a disk of a certain radius, and different columns have different radius. The radius itself is not specified, since only the number of eigenvalues matters when we use the data. Every row represents a random realization of the disorder inside the system. B. Filename: figure.mlx Short description: This .mlx file plots the figures. It should be opened by MatLab. 2. Relationship between files: figure.mlx uses the data containing inside the folder data to generate the plots. 3. Are there multiple versions of the dataset? N -------------------------- METHODOLOGICAL INFORMATION -------------------------- 1. Description of methods used for collection/generation of data: We numerically calculate the number variance $\Sigma^2$ in the three dimensional TME model and study the evolution of $\Sigma^2$ with $W$ as the system goes from a metal to an insulator. We use statistics of complex eigenvalues obtained by diagonalization of the TME model on many realizations of $L \times L \times L$ cubic lattices with $L = 8,12,16$. The diagonalization is done using LAPACK algorithm. Unlike the real spectrum of Hermitian systems, now the eigenvalues are points in the two dimensional complex plane. Therefore, we select a disk of radius $E$ centered at the origin of the complex plane, and study how $\Sigma^2$ depends on the average number of eigenvalues $\ev{N}$ inside such a disk. 2. Methods for processing the data: We calculate the average number and variance from all realizations corresponding to fixed disorder $W$, and then collect all series of variance versus average number at different $W$. 3. Instrument- or software-specific information needed to interpret the data: MatLab. 4. People involved with sample collection, processing, analysis and/or submission: Yi Huang is in charge of all data collection, processing, and analysis. ----------------------------------------- DATA-SPECIFIC INFORMATION FOR: [FILENAME] ----------------------------------------- 1. Number of variables: 5 2. Number of cases/rows: 12000 3. Variable List A. Name: d Description:Dimensionality of the lattice. B. Name: L Description: lattice size (side length). C. Name: W Description: disorder strength. ----------------------------------- Directory Structure ----------------------------------- Copy directory structure. . ├── [ 15K] L8.pdf ├── [ 704] L8and12/ │   ├── [117K] f1_d3_L12_W2.dat │   ├── [117K] f1_d3_L12_W3.dat │   ├── [117K] f1_d3_L12_W4.dat │   ├── [117K] f1_d3_L12_W5.5.dat │   ├── [117K] f1_d3_L12_W5.dat │   ├── [117K] f1_d3_L8_W2.dat │   ├── [117K] f1_d3_L8_W3.dat │   ├── [117K] f1_d3_L8_W4.dat │   ├── [117K] f1_d3_L8_W5.5.dat │   ├── [117K] f1_d3_L8_W5.dat │   ├── [117K] f2_d3_L12_W2.dat │   ├── [117K] f2_d3_L12_W3.dat │   ├── [117K] f2_d3_L12_W4.dat │   ├── [117K] f2_d3_L12_W5.5.dat │   ├── [117K] f2_d3_L12_W5.dat │   ├── [117K] f2_d3_L8_W2.dat │   ├── [117K] f2_d3_L8_W3.dat │   ├── [117K] f2_d3_L8_W4.dat │   ├── [117K] f2_d3_L8_W5.5.dat │   └── [117K] f2_d3_L8_W5.dat ├── [117K] f1_d3_L16_W100.dat ├── [117K] f1_d3_L16_W2.dat ├── [117K] f1_d3_L16_W3.dat ├── [117K] f1_d3_L16_W4.dat ├── [117K] f1_d3_L16_W5.5.dat ├── [117K] f1_d3_L16_W5.dat ├── [115K] f1_d3_L16_W6.5.dat ├── [117K] f1_d3_L16_W6.dat ├── [2.3M] f1_d3_L8_W2.dat ├── [2.3M] f1_d3_L8_W3.dat ├── [2.3M] f1_d3_L8_W4.dat ├── [2.3M] f1_d3_L8_W5.5.dat ├── [2.3M] f1_d3_L8_W5.dat ├── [1.4M] f2_d3_L12_W2.dat ├── [1.4M] f2_d3_L12_W3.dat ├── [1.4M] f2_d3_L12_W4.dat ├── [1.4M] f2_d3_L12_W5.5.dat ├── [1.4M] f2_d3_L12_W5.dat ├── [117K] f2_d3_L16_W100.dat ├── [117K] f2_d3_L16_W2.dat ├── [117K] f2_d3_L16_W3.dat ├── [117K] f2_d3_L16_W4.dat ├── [117K] f2_d3_L16_W5.5.dat ├── [117K] f2_d3_L16_W5.dat ├── [115K] f2_d3_L16_W6.5.dat ├── [117K] f2_d3_L16_W6.dat ├── [ 18K] f2_d3_L25_W2.dat ├── [4.7K] f2_d3_L25_W3.dat ├── [4.6K] f2_d3_L25_W4.dat ├── [4.8K] f2_d3_L25_W6.dat ├── [2.3M] f2_d3_L8_W2.dat ├── [2.3M] f2_d3_L8_W3.dat ├── [2.3M] f2_d3_L8_W4.dat ├── [2.3M] f2_d3_L8_W5.5.dat ├── [2.3M] f2_d3_L8_W5.dat ├── [117K] f_L2500.dat ├── [ 84K] figures.mlx └── [ 640] non-hermitian2/ ├── [2.3K] H_initial.m ├── [ 201] cnh.pbs ├── [ 983] comb_data.m ├── [1015] comb_data_anderson.m ├── [ 233] cqsubmit.sh* ├── [ 780] crop_c.m ├── [ 413] crop_circle.m ├── [ 96] data/ ├── [ 997] gen.sh* ├── [3.2K] my_variance.m ├── [3.1K] my_variance_anderson.m ├── [ 809] neighbor_one.m ├── [ 273] qsubmit.sh* ├── [ 246] rnh.pbs └── [ 12K] sp.pdf 3 directories, 72 files