QMagen (v0.1.0)

Introduction

QMagen is a package for the finite-temperature many-body simulations and an advanced tool for thermal data analysis of magnetic quantum materials. The package consists of two main parts:

Quantum Many-Body Sovlers

Exact diagonalization (ED, as a high-T solver);
Linearized tensor renormalization group (LTRG, as a low-T solver for 1D spin chain materials, etc);
Exponential tensor renormalization group (XTRG, as a low-T solver for quasi-1D and 2D magnets, etc).

Efficient Optimizers

Bayesian optimization.

Try Your First QMagen Program

This program can be used in the following two typical circumstances (and possibly others):

Learning model Hamiltonian by automatically fitting experimental thermal data through the Bayesian optimization:
RunScript/RunOpt.m;
Carrying out many-body calculations on specific model:
RunScript/RunMBSolver.m.

Here we give an example of the automatic parameter searching.

Basic Configuration

To start a QMagen job, one needs to firstly set the following parameters (Para.) in RunScript/RunOpt.m

ManyBodySolver
To choose the many-body solver as 'ED', 'iLTRG' or 'XTRG';
ModelName
To choose the model of material, all the available models are given in SpinModel;
Mode = 'OPT'
To choose the working mode as paremeter searching.

Experimental Data

Import magnetic specific heat (Cm) and susceptibility (Chi) data.

CmDataFile = {'FileName1'; ...}
To set the file name of magnetic specific heat data.
The file should only contains a N-by-2 array where the first column is temperature in Kelvin and the second column is corresponding specific heat with J mol^-1 K^-1.
CmDataTRange = {[T1, T2]; ...}
To set the fitting temperature range of Cm data.
CmDataField = {[B1x, B1y, B1z]; ...}
To give the magentic field strength (in Tesla) of experimental data.
CmDatagInfo = {gNum1; ...} To set use which Lande factor to converse unit. Only required when the Lande factors are not given along Sx, Sy, Sz direction.
ChiDataFile = {'FileName1'; ...}
To set the file name of magnetic susceptibility data.
The file should only contain a N-by-2 array where the firsl column is temperature (in a unit of Kelvin) and the second column lists the corresponding susceptibility data (in the SI unit cm^3 mol^-1).
ChiDataTRange = {[T1, T2]; ...}
To set the fitting temperature range of corresponding Chi data.
ChiDataField = {[B1x, B1y, B1z]; ...}
To give the magentic field strength (Tesla) of experimental data.
ChiDatagInfo = {gNum1; ...} To set use which Lande factor to converse unit. Only required when the Lande factors are not given along Sx, Sy, Sz direction.

Model Information

The lattice geometry and parameter optimization range (called ModelConf.) should be assigned in the file SpinModel/SpinModel_XXX.m.

Lattice
To set the lattice geometry information :
- .L = Inf for 1D systems (currently we only support infinite-size LTRG for 1D)
- .Lx, .Ly, .BCX, .BCY for 2D systems (be reminded we support finite-size XTRG for 2D)
Para_Range{i}
To set the range of ModelConf.Para_Name{i}
- an interval [a, b]
- a fixed value a
- keep it the same as another model parameter 'J'.
gFactor_Range{i}
To set the range of ModelConf.gFactor_Name{i} like above.

Runtime parameters

For beginners, we do not recommend changing the relevant parameters.

RunScript/ImportMBSolverPara.m
To change the parameters of many-body solvers, including ED, LTRG, and XTRG.
RunScript/ImportBOPara.m
To change the parameter of Bayesian optimization.

Loss Function

We have provided several forms of the loss function, which one needs to select in RunScript/RunOpt.m.

LossConf.WeightList
To set the weights of different experimental data.
LossConf.Type
To choose the form of loss function.
LossConf.Design
To adapt the loss function, like log(Loss), so as to improve its performance in parameter searching.

Save Settings

Setting.PLOTFLAG
To decide whether plotting result in each iteration.
Setting.SAVEFLAG
To decide whether save thermal results of each iteration calculated by many-body solver.
Setting.SAVENAME
To set the name of folder saving many-body simulation results in Tmp, including the model informationn and their corresponding thermodynamics data.

Fitting Results

The landscape information of Bayesian optimization will also be stored in Tmp after the specified number of iterations (Para.Group_MaxEval in RunScript/ImportBOPara.m) is finished. The result contains a class BayesianOptimization called res which include parameter and corresponding loss function values at each iterations. To show the landscape estimated by Bayesian optimization one can call PlotScript/LandscapePlot.m.

Maintainer

Yuan Gao, Beihang University
mail: 17231064@buaa.edu.cn
Bin-Bin Chen, Beihang University
mail: bunbun@buaa.edu.cn
Wei Li, Beihang University & ITP-CAS
mail: w.li@buaa.edu.cn

Citation

If you use QMagen in teaching and research, please cite the following related works:

@article{QMagen2020,
  title={Learning the Effective Spin Hamiltonian of a Quantum Magnet},
  author={Sizhuo Yu, Yuan Gao, Bin-Bin Chen and Wei Li},
  journal={arXiv preprint arXiv:2011.12282},
  year={2020}
}

@article{LTRG2011,
  title = {Linearized Tensor Renormalization Group Algorithm for the Calculation of Thermodynamic Properties of Quantum Lattice Models},
  author = {Li, W. and Ran, S.-J. and Gong, S.-S. and Zhao, Y. and Xi, B. and Ye, F. and Su, G.},
  journal = {Phys. Rev. Lett.},
  volume = {106},
  issue = {12},
  pages = {127202},
  numpages = {4},
  year = {2011},
  month = {Mar},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.106.127202},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.106.127202}
}

@article{BilayerLTRG2017,
	Author = {Dong, Y.-L. and Chen, L. and Liu, Y.-J. and Li, W.},
	Doi = {10.1103/PhysRevB.95.144428},
	Issue = {14},
	Journal = {Phys. Rev. B},
	Month = {Apr},
	Numpages = {10},
	Pages = {144428},
	Publisher = {American Physical Society},
	Title = {Bilayer linearized tensor renormalization group approach for thermal tensor networks},
	Url = {https://link.aps.org/doi/10.1103/PhysRevB.95.144428},
	Volume = {95},
	Year = {2017},
	Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.95.144428},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevB.95.144428}
}

@article{SETTN2017,
	Author = {Chen, B.-B. and Liu, Y.-J. and Chen, Z. and Li, W.},
	Doi = {10.1103/PhysRevB.95.161104},
	Issue = {16},
	Journal = {Phys. Rev. B},
	Month = {Apr},
	Numpages = {5},
	Pages = {161104(R)},
	Publisher = {American Physical Society},
	Title = {Series-expansion thermal tensor network approach for quantum lattice models},
	Url = {https://link.aps.org/doi/10.1103/PhysRevB.95.161104},
	Volume = {95},
	Year = {2017},
	Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.95.161104},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevB.95.161104}
}

@Article{XTRG2018,
  title = {Exponential Thermal Tensor Network Approach for Quantum Lattice Models},
  author = {Chen, B.-B. and Chen, L. and Chen, Z. and Li, W. and Weichselbaum, A.},
  journal = {Phys. Rev. X},
  volume = {8},
  issue = {3},
  pages = {031082},
  numpages = {29},
  year = {2018},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevX.8.031082},
  url = {https://link.aps.org/doi/10.1103/PhysRevX.8.031082}
}

@article{XTRG2019,
  title = {Thermal tensor renormalization group simulations of square-lattice quantum spin models},
  author = {Li, H. and Chen, B.-B. and Chen, Z. and von Delft, J. and Weichselbaum, A. and Li, W.},
  journal = {Phys. Rev. B},
  volume = {100},
  issue = {4},
  pages = {045110},
  numpages = {17},
  year = {2019},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.100.045110},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.100.045110}
}

vegaandagev / QMagen