Algorithms for finite projected entangled pair states
By Michael Lubasch, J. I. Cirac, M. Bañuls. 2014
153 citations recorded by the source corpus.
Projected Entangled Pair States (PEPS) are a promising ansatz for the study of strongly correlated quantum many-body systems in two dimensions. But due to their high computational cost, developing and improving PEPS algorithms is necessary to make the ansatz widely usable in practice. Here we analyze several algorithmic aspects of the method. On the one hand, we quantify the connection between the correlation length of the PEPS and the accuracy of its approximate contraction, and discuss how purifications can be used in the latter. On the other, we present algorithmic improvements for the update of the tensor that introduce drastic gains in the numerical conditioning and the efficiency of the algorithms. Finally, the state-of-the-art general PEPS code is benchmarked with the Heisenberg and quantum Ising models on lattices of up to $21 \times 21$ sites.
View Paper: https://www.semanticscholar.org/paper/b96d2b1a29d61adbeb14db7555dafba27b338756
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- L. Vanderstraeten
- J. Haegeman
- Frank Verstraete
- Jacob C. Bridgeman
- Marcello Dalmonte
- Christopher T. Chubb
- Simone Montangero
- Philippe Corboz
Citations in the corpus
- Lattice gauge theory simulations in the quantum information era (2016, background): “states [71]; while mixed states can be described either by matrix product operators (MPO) which also efficiently represent a large class of operators (many-bodyHamiltonians or time evolution operators) [72], or by locally pu-”
- Hand-waving and interpretive dance: an introductory course on tensor networks (2016, background): “Tensor network states therefore provide an important analytic framework for understanding the universal properties of classes of states which possess particular properties, such as those which only support certain entanglement or correlation structures.”
- Gradient methods for variational optimization of projected entangled-pair states (2016, methodology): “This problem was solved by regularizing the environment appropriately and fixing the gauge of the PEPS tensor [20,34].”