Gradient methods for variational optimization of projected entangled-pair states
- Author
- Laurens Vanderstraeten (UGent) , Jutho Haegeman (UGent) , Philippe Corboz and Frank Verstraete (UGent)
- Organization
- Project
-
- QUTE (Quantum tensor networks and entanglement)
- Abstract
- 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.
- Keywords
- MATRIX RENORMALIZATION-GROUP, SPIN-1/2 HEISENBERG-ANTIFERROMAGNET, GROUND-STATE, PARAMETERS, SYSTEMS, LATTICE, MODEL
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8152448
- MLA
- Vanderstraeten, Laurens, et al. “Gradient Methods for Variational Optimization of Projected Entangled-Pair States.” PHYSICAL REVIEW B, vol. 94, no. 15, 2016, doi:10.1103/PhysRevB.94.155123.
- APA
- Vanderstraeten, L., Haegeman, J., Corboz, P., & Verstraete, F. (2016). Gradient methods for variational optimization of projected entangled-pair states. PHYSICAL REVIEW B, 94(15). https://doi.org/10.1103/PhysRevB.94.155123
- Chicago author-date
- Vanderstraeten, Laurens, Jutho Haegeman, Philippe Corboz, and Frank Verstraete. 2016. “Gradient Methods for Variational Optimization of Projected Entangled-Pair States.” PHYSICAL REVIEW B 94 (15). https://doi.org/10.1103/PhysRevB.94.155123.
- Chicago author-date (all authors)
- Vanderstraeten, Laurens, Jutho Haegeman, Philippe Corboz, and Frank Verstraete. 2016. “Gradient Methods for Variational Optimization of Projected Entangled-Pair States.” PHYSICAL REVIEW B 94 (15). doi:10.1103/PhysRevB.94.155123.
- Vancouver
- 1.Vanderstraeten L, Haegeman J, Corboz P, Verstraete F. Gradient methods for variational optimization of projected entangled-pair states. PHYSICAL REVIEW B. 2016;94(15).
- IEEE
- [1]L. Vanderstraeten, J. Haegeman, P. Corboz, and F. Verstraete, “Gradient methods for variational optimization of projected entangled-pair states,” PHYSICAL REVIEW B, vol. 94, no. 15, 2016.
@article{8152448,
abstract = {{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.}},
articleno = {{155123}},
author = {{Vanderstraeten, Laurens and Haegeman, Jutho and Corboz, Philippe and Verstraete, Frank}},
issn = {{2469-9950}},
journal = {{PHYSICAL REVIEW B}},
keywords = {{MATRIX RENORMALIZATION-GROUP,SPIN-1/2 HEISENBERG-ANTIFERROMAGNET,GROUND-STATE,PARAMETERS,SYSTEMS,LATTICE,MODEL}},
language = {{eng}},
number = {{15}},
pages = {{14}},
title = {{Gradient methods for variational optimization of projected entangled-pair states}},
url = {{http://doi.org/10.1103/PhysRevB.94.155123}},
volume = {{94}},
year = {{2016}},
}
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