Dataset Overview

This dataset contains numerical outputs used to reproduce Figure 1 of the associated manuscript on fractional Chern insulators and their relationship to band geometry. The data are provided as two whitespace-delimited plain-text files:

• checkerboard_3x6_fixed.out
• kagome_3x6_fixed.out

Each file corresponds to a different lattice model. The checkerboard file contains data for the checkerboard lattice model, and the kagome file contains data for the kagome lattice model. Each row represents one sampled point in the parameter space of each model. Each file contains 1,000,000 rows and 6 numerical columns.

The files are intended to support reproduction of the manuscript's Figure 1 and to enable reuse for related analyses, including comparisons between fractional Chern insulator quality and single-particle band-geometry indicators.

Associated Manuscript

These data are associated with the manuscript available at:

https://arxiv.org/pdf/2512.01873

The dataset README focuses on the structure, meaning, and reuse of the data files. For full theoretical definitions, model Hamiltonians, parameter-generation procedures, and scientific interpretation, users should consult the associated manuscript.

File List

checkerboard_3x6_fixed.out

Data for the checkerboard lattice model. This file is used to reproduce Figure 1a of the associated manuscript.

• Format: whitespace-delimited plain text
• Number of rows: 1,000,000
• Number of columns: 6
• Units: all columns are dimensionless or expressed in the natural numerical units of the lattice model calculation

kagome_3x6_fixed.out

Data for the kagome lattice model. This file is used to reproduce Figure 1b of the associated manuscript.

• Format: whitespace-delimited plain text
• Number of rows: 1,000,000
• Number of columns: 6
• Units: all columns are dimensionless or expressed in the natural numerical units of the lattice model calculation

Data Format

Both files have the same column structure. Rows are independent sampled parameter points. Columns are ordered as follows:

Column Definitions and Interpretation

Column 1: Fractional Chern insulator quality metric \L

Column 1 gives the signed fractional Chern insulator quality metric for each sampled parameter point. It is computed as the maximum of the two flux-resolved metrics:

column 1 = maximum(column 2, column 3)

This means that the reported quality metric is determined by the less favorable of the two tested flux sectors. In the associated manuscript, this metric is used as the color variable in Figure 1.

Important interpretation notes:

• \L is signed.
• Negative \L values indicate parameter points for which the ground state is a fractional Chern insulator, with larger values indicating larger many-body gaps
• Positive \L values encode a spectral distance from a fractional Chern insulator.
• For visualization, a signed-log or symmetric-log color scale should be used if logarithmic color compression is desired.

Column 2: Flux-resolved metric at \Phi = 0

Column 2 gives the flux-resolved fractional Chern insulator metric evaluated at flux \Phi = zero. This column is one of the two inputs used to compute column 1.

Important interpretation notes:

• Values may be positive or negative.
• This column should be interpreted together with column 3, because column 1 uses the maximum of the two flux-resolved values.

Column 3: Flux-resolved metric at \Phi = \pi

Column 3 gives the flux-resolved fractional Chern insulator metric evaluated at boundary flux \Phi equals \pi. This column is the second input used to compute column 1.

Important interpretation notes:

• Values may be positive or negative.
• This column should be interpreted together with column 2, because column 1 uses the maximum of the two flux-resolved values.

Column 4: Single-particle gap

Column 4 gives the single-particle band gap for each sampled parameter point. The gap is a single-particle quantity and is distinct from the many-body fractional Chern insulator quality metric.

Important interpretation notes:

• Values are positive in the submitted files.
• This column is included for reuse in analyses comparing band gap, band geometry, and fractional Chern insulator quality.
• In Figure 1 of the associated manuscript, this column is not used as either the horizontal or vertical axis.

Column 5: Trace-condition violation \T

Column 5 gives the trace-condition violation. The trace condition is a band-geometry criterion that can be used as a single-particle indicator of whether a band may be favorable for fractional Chern insulators.

Important interpretation notes:

• Values are positive in the submitted files.
• Smaller values indicate a smaller violation of the trace condition.
• In Figure 1 of the associated manuscript, this column is plotted on one logarithmic axis.
• Because values are positive, an ordinary logarithmic axis can be used for visualization.

Column 6: Berry-curvature fluctuation \sigma sub B

Column 6 gives the Berry-curvature fluctuation. Berry curvature is a geometric property of a single-particle band, also sometimes associated with the stability of a fractional Chern insulator. This column measures how much the Berry curvature varies across momentum space.

Important interpretation notes:

• Values are positive in the submitted files.
• In Figure 1 of the associated manuscript, this column is plotted on one logarithmic axis.
• Because values are positive, an ordinary logarithmic axis can be used for visualization.

Reproducing Figure 1

To reproduce the main structure of Figure 1:

1. Load either checkerboard_3x6_fixed.out or kagome_3x6_fixed.out as a numerical array with 6 columns.
2. Use column 5, trace_violation, as one log-scaled axis.
3. Use column 6, berry_curvature_fluctuation, as the other log-scaled axis.
4. Use column 1, FCI_quality_metric, as the color variable.
5. Use a signed-log or symmetric-log color scale for column 1, because the fractional Chern insulator quality metric can be negative.

The checkerboard file corresponds to Figure 1a. The kagome file corresponds to Figure 1b.

Example Loading Code

The files can be loaded using standard numerical software. For example, in Python:

import numpy as np

data = np.loadtxt("checkerboard_3x6_fixed.out")

FCI_quality_metric = data[:, 0]
FCI_flux_metric_Phi_0 = data[:, 1]
FCI_flux_metric_Phi_pi = data[:, 2]
single_particle_gap = data[:, 3]
trace_violation = data[:, 4]
berry_curvature_fluctuation = data[:, 5]

Users can check the relation between the first three columns with:

np.allclose(FCI_quality_metric, np.maximum(FCI_flux_metric_Phi_0, FCI_flux_metric_Phi_pi))

This should return True.

Value Ranges in the Submitted Files

Approximate observed ranges are listed below to help users identify parsing errors or accidental column swaps.

Columns 2 and 3 can have wider negative tails than column 1 because column 1 is the maximum of columns 2 and 3.

Units

The submitted columns are numerical outputs from lattice-model calculations. They should be treated as dimensionless quantities or as values in the natural units used by the corresponding model calculation. No physical unit conversion is required to reproduce the manuscript's Figure 1.

Missing Data and Quality Checks

The submitted files do not include a header row and do not use missing-value markers. A basic quality check performed on the files found:

• 1,000,000 rows in each file
• 6 columns in each row
• finite numerical values in all entries
• column 1 exactly equal to the maximum of columns 2 and 3 for every row
• positive values in columns 4, 5, and 6 for every row

Users should verify these properties after downloading the files, especially if the files are transferred between systems or converted to another format.

Reuse Potential

These data may be reused for:

• reproducing Figure 1 of the associated manuscript
• benchmarking alternative fractional Chern insulator screening metrics
• testing correlations between single-particle band geometry and many-body diagnostics
• developing or validating machine-learning models for identifying promising parameter regimes
• comparing the checkerboard and kagome lattice models under common data conventions
• exploring visualization methods for signed quality metrics over log-scaled geometric indicators

When reusing the data, users should preserve the column order and the signed interpretation of \L.

Legal and Ethical Considerations

These data are synthetic numerical outputs from computational lattice-model calculations. They do not contain personal information, human-subject data, protected health information, ecological location data, culturally sensitive information, or other sensitive data types.

Users should cite the associated manuscript and dataset record when reusing these files. Users should also retain the column definitions in this README when redistributing derived versions of the data.

Recommended Citation

Please cite the associated manuscript and the dataset repository or archive record where these files are deposited. If a formal dataset DOI is assigned, cite that DOI in addition to the manuscript.