Gradient methods for variational optimization of projected entangled-pair states
By L. Vanderstraeten, J. Haegeman, Philippe Corboz, Frank Verstraete. 2016
152 citations recorded by the source corpus.
We present a conjugate-gradient method for the ground-state optimization of projected entangled-pair states (PEPS) in the thermodynamic limit, as a direct implementation of the variational principle within the PEPS manifold. Our optimization is based on an efficient and accurate evaluation of the gradient of the global energy functional by using effective corner environments, and is robust with respect to the initial starting points. It has the additional advantage that physical and virtual symmetries can be straightforwardly implemented. We provide the tools to compute static structure factors directly in momentum space, as well as the variance of the Hamiltonian. We benchmark our method on Ising and Heisenberg models, and show a significant improvement on the energies and order parameters as compared to algorithms based on imaginary-time evolution.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/4af85ca42a3ce01d39cf7da394d5659adb7a96d7
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- M. Fishman
- S. White
- J. Haegeman
- E. Stoudenmire
- L. Vanderstraeten
- Frank Verstraete
- Andrew J. Daley
- Pasquale Calabrese
In Atomic and Molecular Physics, and Optics
- M. Fishman
- E. Stoudenmire
- S. White
- L. Vanderstraeten
- Frank Verstraete
- J. Haegeman
- Andrew J. Daley
- Frank Pollmann
In Condensed Matter Physics
- L. Vanderstraeten
- E. Stoudenmire
- J. Haegeman
- Frank Verstraete
- M. Fishman
- S. White
- Frank Pollmann
- Andrew J. Daley
Citations in the corpus
- Tangent-space methods for uniform matrix product states (2018, background): “[83, 84] that aim to optimize the energy density in the thermodynamic limit directly.”
- The ITensor Software Library for Tensor Network Calculations (2020, methodology): “Algorithms and methods for optimizing PEPS have reached a point of maturity such that there are now a handful of essentially standard approaches, such as variational iPEPS [74, 92, 93] and fixed-point methods for computing PEPS environment tensors [71].”