T-Nalg: Tensor Netwok Algorithms for EVERYONE

• Other contributor(s): Xi Chen (https://github.com/lumberjack0101)
• The aim of EasyStartDMRG is to let everyone be able to use tensor network algorithms to simulate the models of its own interests
• If our code helps your project, please cite our tensor network review paper: S. J. Ran, et al., arXiv.1708.09213. (https://arxiv.org/abs/1708.09213) and this webpage. Thank you very much!
• Before using, you need to install numpy, scipy, termcolor, ipdb, matplotlib, and multiprocessing in your python

DMRG for any finite-size lattices

Two ways of using DMRG:

1. Set up Parameters.py and run dmrg_finite_size in DMRG_anyH.py
   >>> import DMRG_anyH as DMRG
   >>> DMRG.dmrg_finite_size()
2. Run EasyStartDMRG directly
   >>> import EasyStart_DMRG
   >>> EasyStart_DMRG

To use EasyStartDMRG, you only need to know three things:

1.What you are simulating (e.g., Heisenber model, entanglement, ect.)    
2.How to run a Python code   
3.English   
* It is ok if you may not know how DMRG works   

Steps to use EasyStartDMRG:

1.Run 'EasyStart_DMRG'   
2.Input the parameters by following the instructions 
3.Choose the quantities you are interested in 

Use DMRG by writing a script and editing Parameters.py

See an example in "testDMRG.py".

Some notes:

1.Your parameters are saved in '.\para_dmrg\_para.pr' 
2.To read *.pr, use function 'load_pr' in 'Basic_functions_SJR.py' 
3.The results including the MPS will be save in '.\data_dmrg' 

Models that can be computed:

1. Spin-1/2 models on any finite-size lattices
2. Bosonic models on any finite-size lattices (need to munually perpare Parameters.py)

Physics that can be computed:

1. Ground states in MPS form
2. Ground-state average of any one-body operator
3. Ground-state average of any two-body operator

Contents to be added soon

1. Higher-spin models
2. iDMRG [1] and iTEBD [2] for the ground states of infinite spin chains
3. LTRG [3] for the thermodynamics of infinite spin chains
4. Simple update [4] for the ground states of infinite 2D spin models
5. ODTNS [5] for the thermodynamics of infinite 2D spin models
6. AOP [6, 7] for the ground states of 1D, 2D, 3D infinite models
7. AOP [8] for the thermodynamics of 1D, 2D, 3D infinite models

References

[0] Our TN review: Shi-Ju Ran, Emanuele Tirrito, Cheng Peng, Xi Chen, Gang Su, Maciej Lewenstein. Review of Tensor Network Contraction Approaches, arXiv:1708.09213.
[1] iDMRG: Steven R. White. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 69, 2863 (1992).
[2] iTEBD: Guifre Vidal. Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension. Phys. Rev. Lett. 98, 070201 (2007).
[3] LTRG: Wei Li, Shi-Ju Ran, Shou-Shu Gong, Yang Zhao, Bin Xi, Fei Ye, and Gang Su. Linearized tensor renormalization group algorithm for the calculation of thermodynamic properties of quantum lattice models. Phys. Rev. Lett. 106, 127202 (2011).
[4] Simple update: Hong-Chen Jiang, Zheng-Yu Weng, and Tao Xiang. Accurate determination of tensor network state of quantum lattice models in two dimensions. Phys. Rev. Lett. 101, 090603 (2008).
[5] ODTNS: Shi-Ju Ran, Wei Li, Bin Xi, Zhe Zhang, and Gang Su. Optimized decimation of tensor networks with super-orthogonalization for two-dimensional quantum lattice models. Phys. Rev. B 86, 134429 (2012).
[6] AOP (1D): Shi-Ju Ran. Ab initio optimization principle for the ground states of translationally invariant strongly-correlated quantum lattice models. Phys. Rev. E 93, 053310 (2016).
[7] AOP (2D and 3D): Shi-Ju Ran, Angelo Piga, Cheng Peng, Gang Su, and Maciej Lewenstein. Few-body systems capture many-body physics: Tensor network approach. Phys. Rev. B 96, 155120 (2017).
[8] AOP (finite-temperature): Shi-Ju Ran, et al., in preparation.