by Juraj Hasik, Glen Bigan Mbeng
peps-torch performs optimization of infinite Projected entangled-pair states (iPEPS)
by direct energy minimization. The energy is evaluated using environments obtained
by the corner-transfer matrix (CTM) algorithm. Afterwards, the gradients are computed by reverse-mode
automatic differentiation (AD).
For the full documentation, continue to peps-torch.readthedocs.io
Optimize one-site (C4v) symmetric iPEPS with bond dimension D=2 and environment dimension X=32 for J1-J2 model at J2/J1=0.3 run
python examples/optim_j1j2_c4v.py --bond_dim 2 --chi 32 --seed 123 --j2 0.3 --out_prefix ex-c4v
Using the resulting state ex_state.json, compute the observables such as spin-spin
and dimer-dimer correlations for distance up to 20 sites
python examples/ctmrg_j1j2_c4v.py --instate ex-c4v_state.json --chi 48 --j2 0.3 --corrf_r 20
To instead optimize iPEPS with 2x2 unit cell containing four distinct on-site tensors run
python examples/optim_j1j2.py --tiling 4SITE --bond_dim 2 --chi 32 --seed 123 --j2 0.3 --CTMARGS_fwd_checkpoint_move --OPTARGS_tolerance_grad 1.0e-8 --out_prefix ex-4site
The memory requirements of AD would increase sharply if all the intermediate variables are stored.
Instead, by passing -CTMARGS_fwd_checkpoint_move flag we opt for recomputing them on the fly
while saving only the intermediate tensors of CTM environment.
Compute observables and spin-spin correlation functions in horizontal and vertical direction of the resulting state
python examples/ctmrg_j1j2.py --tiling 4SITE --chi 48 --j2 0.3 --instate ex-4site_state.json --corrf_r 20
- spin systems
- arbitrary rectangular unit cells
- only real-valued tensors
- PyTorch 1.+ (see https://pytorch.org/)
- (optional) scipy 1.3.+
- PyTorch 1.+
- sphinx
- sphinx_rtd_theme
All the dependencies can be installed through conda (see https://docs.conda.io).
Afterwards, build documentation as follows:
cd docs && make html
The generated documentation is found at docs/build/html/index.html
Inspired by the pioneering work of Hai-Jun Liao, Jin-Guo Liu, Lei Wang, and Tao Xiang,
Phys. Rev. X 9, 031041 or arXiv version arXiv:1903.09650
References:
- Corner Transfer Matrix Renormalization Group Method, T. Nishino and K. Okunishi, Journal of the Physical Society of Japan 65, 891 (1996) or arXiv version arXiv:cond-mat/9507087
- Faster Methods for Contracting Infinite 2D Tensor Networks,
M.T. Fishman, L. Vanderstraeten, V. Zauner-Stauber, J. Haegeman, and F. Verstraete, Phys. Rev. B 98, 235148 (2018) or arXiv version arXiv:1711.05881 - Competing States in the t-J Model: Uniform d-Wave State versus Stripe State (Supplemental Material), P. Corboz, T. M. Rice, and M. Troyer, Phys. Rev. Lett. 113, 046402 (2014) or arXiv version arXiv:1402.2859