This README.txt file was generated on 2025-08-18 by Ethan McGarrigle.

GENERAL INFORMATION

Date of data collection: 2025-07-01 through 2025-08-01

Geographic location of data collection: University of California Santa Barbara, Santa Barbara, California, USA

Information about funding sources that supported the collection of the data: This work was enabled by field-theoretic simulation tools developed under support from the National Science Foundation (CMMT Program, DMR-2104255). Use was made of computational facilities purchased with funds from the NSF (CNS-1725797) and administered by the Center for Scientific Computing (CSC). This work made use of the BioPACIFIC Materials Innovation Platform computing resources of the National Science Foundation Award No. DMR-1933487. The CSC is supported by the California NanoSystems Institute and the Materials Research Science and Engineering Center (MRSEC; NSF DMR 2308708) at UC Santa Barbara. Ethan McGarrigle acknowledges support from a Mitsubishi Chemical Fellowship. Thomas Kiely acknowledges support from the National Science Foundation under grant PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP), and from the Gordon and Betty Moore Foundation through Grant GBMF8690 to the University of California, Santa Barbara.

SHARING/ACCESS INFORMATION

Links to publications that cite or use the data: https://arxiv.org/abs/2508.11057
Recommended citation for this dataset: https://doi.org/10.48550/arXiv.2508.11057

DATA & FILE OVERVIEW

File list: Files are organized based on figure number from the corresponding manuscript and simulation method used to generate the data. There are two figures. Each figure has the files "FigureX_Primitive_data.csv" and "FigureX_ExactPropagator_data.csv" are found with the same formatting and data. Files labelled "Primitive" contain data using the previous coherent state complex Langevin simulation method, which leveraged a primitive approximation within the path integral derivation. Files labelled "ExactPropagator" leverage the new technique detailed in the corresponding manuscript, where the quadratic portion of the propagator is applied in an exact manner during the path integral derivation. The files are listed here:

Figure1_Primitive_data.csv
Figure1_ExactPropagator_data.csv
Figure2_Primitive_data.csv
Figure2_ExactPropagator_data.csv

A. Figure1: Imaginary time convergence for a Bose fluid 
	1. Columns: Imaginary time points (N_{\tau}), average particle number, standard error for particle number, intensive canonical internal energy, standard error for intensive canonical internal energy, intensive free energy, standard error for intensive free energy 
	2. Filename denotes which path-integral technique was used to generate the data. 

B. Figure2: Imaginary time convergence for a Rashba spin-orbit coupled Bose fluid 
	1. Columns: Imaginary time points (N_{\tau}), average particle number for upspin particles, standard error for upspin particle number, intensive canonical internal energy, standard error for intensive canonical internal energy, intensive free energy, standard error for intensive free energy 
	2. Filename denotes which path-integral technique was used to generate the data. 

METHODOLOGICAL INFORMATION

Description of methods used for collection/generation of data:
Some data were generated using an improved coherent state complex Langevin method, detailed in our preprint: https://arxiv.org/abs/2508.11057 .
Some data were generated using previous coherent state complex Langevin simulation methods, developed in the following publications:
https://doi.org/10.1103/PhysRevLett.131.173403
https://doi.org/10.1103/PhysRevLett.124.070601

Methods for processing the data: Thermodynamic quantities were computed using field-operator functionals during the simulation, producing samples at some printing frequency. Statistics were taken for each thermodynamic quantity after an initial method equilibration period, producing a mean and a standard error of the mean, which are plotted in Figures 1 and 2.

Describe any quality-assurance procedures performed on the data: After the simulation code was tested thoroughly to ensure that it agreed with known thermodynamic results, we generated each data set twice to ensure the results were consistent and statistically significant.

People involved with sample collection, processing, analysis and/or submission: Ethan McGarrigle

DATA-SPECIFIC INFORMATION FOR: Figure1_ExactPropagator_data.csv

1. Number of variables: 7
2. Number of cases/rows: 33
3. Variable List:
   Column 1: Ntau, Number of imaginary time points used
   Column 2: Average particle number, units = number of particles
   Column 3: Standard error of the mean for the particle number, units = number of particles
   Column 4: Dimensionless intensive canonical internal energy, units = dimensionless intensive energy per system area
   Column 5: Standard error of the mean for the intensive canonical internal energy, units = dimensionless energy per system area
   Column 6: Dimensionless intensive free energy, units = dimensionless intensive free energy per system area
   Column 7: Standard error of the mean for the dimensionless intensive free energy, units = dimensionless intensive free energy per system area
4. Missing data codes:
   nan: "Not a number", referring to simulations that diverged (field values blow up to infinite values, which cannot be represented meaningfully with a floating point number. The occurrence of "nan" represents conditions where the simulation technique fails.
5. Specialized formats or other abbreviations used: N/A
6. Notes: Data here utilized the exact quadratic propagator method that was introduced in this manuscript for coherent state, complex Langevin simulations of a one-component Bose fluid in two dimensions.

DATA-SPECIFIC INFORMATION FOR: Figure1_Primitive_data.csv

1. Number of variables: 7
2. Number of cases/rows: 33
3. Variable List:
   Column 1: Ntau, Number of imaginary time points used
   Column 2: Average particle number, units = number of particles
   Column 3: Standard error of the mean for the particle number, units = number of particles
   Column 4: Dimensionless intensive canonical internal energy, units = dimensionless intensive energy per system area
   Column 5: Standard error of the mean for the intensive canonical internal energy, units = dimensionless energy per system area
   Column 6: Dimensionless intensive free energy, units = dimensionless intensive free energy per system area
   Column 7: Standard error of the mean for the dimensionless intensive free energy, units = dimensionless intensive free energy per system area
4. Missing data codes:
   nan: "Not a number", referring to simulations that diverged (field values blow up to infinite values, which cannot be represented meaningfully with a floating point number. Occurrence of "nan" represent conditions where the simulation technique fails.
5. Specialized formats or other abbreviations used: N/A
6. Notes: Data here utilized the primitive propagator method for coherent state, complex Langevin simulations of a one-component Bose fluid in two dimensions.

DATA-SPECIFIC INFORMATION FOR: Figure2_ExactPropagator_data.csv

1. Number of variables: 7
2. Number of cases/rows: 40
3. Variable List:
   Column 1: Ntau, Number of imaginary time points used
   Column 2: Average up-spin particle number, units = number of particles
   Column 3: Standard error of the mean for the up-spin particle number, units = number of particles
   Column 4: Dimensionless intensive canonical internal energy, units = dimensionless intensive energy per system area
   Column 5: Standard error of the mean for the intensive canonical internal energy, units = dimensionless energy per system area
   Column 6: Dimensionless intensive free energy, units = dimensionless intensive free energy per system area
   Column 7: Standard error of the mean for the dimensionless intensive free energy, units = dimensionless intensive free energy per system area
4. Missing data codes:
   nan: "Not a number", referring to simulations that diverged (field values blow up to infinite values, which cannot be represented meaningfully with a floating point number. Occurrence of "nan" represent conditions where the simulation technique fails.
5. Specialized formats or other abbreviations used: N/A
6. Notes: Data here utilized the exact quadratic propagator method that was introduced in this manuscript for coherent state, complex Langevin simulations of a two-component Bose fluid with Rashba spin-orbit coupling in two dimensions.

DATA-SPECIFIC INFORMATION FOR: Figure2_Primitive_data.csv

1. Number of variables: 7
2. Number of cases/rows: 40
3. Variable List:
   Column 1: Ntau, Number of imaginary time points used
   Column 2: Average up-spin particle number, units = number of particles
   Column 3: Standard error of the mean for the up-spin particle number, units = number of particles
   Column 4: Dimensionless intensive canonical internal energy, units = dimensionless intensive energy per system area
   Column 5: Standard error of the mean for the intensive canonical internal energy, units = dimensionless energy per system area
   Column 6: Dimensionless intensive free energy, units = dimensionless intensive free energy per system area
   Column 7: Standard error of the mean for the dimensionless intensive free energy, units = dimensionless intensive free energy per system area
4. Missing data codes:
   nan: "Not a number", referring to simulations that diverged (field values blow up to infinite values, which cannot be represented meaningfully with a floating point number. Occurrence of "nan" represent conditions where the simulation technique fails.
5. Specialized formats or other abbreviations used: N/A
6. Notes: Data here utilized the primitive propagator method for coherent state, complex Langevin simulations of a two-component Bose fluid with Rashba spin-orbit coupling in two dimensions.