Differentiable Programming Tensor Networks
Run this to compute the energy and specific heat of the 2D classical Ising model using Automatic Differentiation through the Tensor Renormalization Group contraction.
$ cd 1_ising_TRG$ python ising.py
Run this to optimize an iPEPS wave function for 2D quantum Heisenberg model. Here, we use Corner Transfer Matrix Renormalization Group for contraction, and L-BFGS for optimization.
$ cd 2_variational_iPEPS$ python variational.py -D 3 -chi 30
You can supply the command line argument -use_checkpoint to reduce the memory usage. To make use of the GPU, you can add -cuda <GPUID>. You will reach the state-of-the-art variational energy and staggered magnetization using this code. You can also supply your own Hamiltonian of interest. In case of a question, you can type python variational.py -h.
Reverse mode AD computes gradient accurately and efficiently for you! Check the codes in adlib for backward functions which propagate gradients through tensor network contractions.
@article{PhysRevX.9.031041,title = {Differentiable Programming Tensor Networks},author = {Liao, Hai-Jun and Liu, Jin-Guo and Wang, Lei and Xiang, Tao},journal = {Phys. Rev. X},volume = {9},issue = {3},pages = {031041},numpages = {12},year = {2019},month = {Sep},publisher = {American Physical Society},doi = {10.1103/PhysRevX.9.031041},url = {https://link.aps.org/doi/10.1103/PhysRevX.9.031041}}