Data Supplement for "Phase diagram of compressible and paired states in the quarter-filled Landau level"

Description: This dataset provides supplemental data for the paper Arxiv 2408.08354, specifically the Density Correlation Function (DCF) and Harmonic Coefficients GkG_kGk (Pol) for various fractional quantum Hall wave functions, as outlined in the paper.

Contents:

• Density Correlation Function (DCF): Corresponds to Eq. (4) in the paper, capturing correlation behavior in fractional quantum Hall systems.
• Harmonic Coefficients Gk (Pol): Corresponds to Eq. (5), representing harmonics relevant to polarization effects.

File Structure:

The data files follow the structure:

• DCF[WF_name, Ne, Nc] and Pol[WF_name, Ne, Nc]:
  • WF_name: Identifier for the wave function (details below).
  • Ne: Number of particles.
  • Nc: Lowest Landau level projection cutoff used in Eq. (C5), if projection is needed.

Data Format:

The data is formatted for Mathematica, with each entry stored as a comma-separated list enclosed in curly braces {}. Each function entry is structured as:

• DCF[WF_name, Ne, Nc] = {value, ...} and Pol[WF_name, Ne, Nc] = {value, ...}

Error Estimation:

For error assessment, each wave function's data is divided into 20 batches. Each batch is averaged separately:

• DCFbatch[WF_name, Ne, Nc, id] and Polbatch[WF_name, Ne, Nc, id]:
  • id: Batch number ranging from 1 to 20.

Wave Function Naming Conventions:

The naming convention used in WF_name designates the state as follows:

• First Letter: Filling factor

  • H: Half-filled
  • Q: Quarter-filled

• Second and Third Letters: Pairing channel (shift)

  • AP: Anti-Pfaffian (l=−3)
  • PH: PH-Pfaffian (l=−1)
  • MR: Moore-Read (l=1)
  • FW: f-wave (l=3)
  • Q0: CFL only (l=0)

• Ending Type: Wave function type

  • S: Paired state with single-particle projection.
  • CFL: Composite Fermi liquid.
  • E: Exact wave function for Moore-Read.

Examples:

• QAPS: Quarter-filled Anti-Pfaffian wave function.
• HPHCFL: Half-filled Composite Fermi liquid at PH-Pfaffian shift.
• QMRE: Quarter-filled Moore-Read exact wave function without expansion of pairing function.

Naming Exceptions:

• La: Laughlin state at ν=1/3.
• QSU2: SU(2)2_2 wave function, Eq. (20) with + sign at ν=1/4 (p=2).
• HASU2 and QASU2: SU(2)2_2 wave function, Eq. (20) with - sign at ν=1/2 and ν=1/4 (p=1 and 2).