Variational optimization with infinite projected entangled-pair states

By Philippe Corboz. 2016

208 citations recorded by the source corpus.

An infinite projected entangled-pair state (iPEPS) is a powerful variational tensor network ansatz for two-dimensional ground states in the thermodynamic limit, and can be seen as a natural generalization of a matrix-product state to two dimensions. One of the main challenges in iPEPS simulations is the optimization of the tensors, i.e., finding the optimal variational parameters, in order to have the best representation of the ground state of a given Hamiltonian. The author presents a variational optimization scheme, in which the energy is minimized in an iterative way by sweeping over all the tensors in the ansatz, in a similar spirit as done in the density-matrix renormalization group method. Benchmark results for challenging problems are presented that show that the variational scheme yields considerably more accurate results than the previously best imaginary-time evolution algorithm, with a similar computational cost and with a faster convergence towards the ground state.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c048a7c3198850f020e08461f3c5c1d3c220766f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. M. Fishman
2. E. Stoudenmire
3. S. White
4. L. Vanderstraeten
5. Frank Verstraete
6. J. Haegeman
7. Andrew J. Daley
8. Frank Pollmann

In Computational Mathematics

1. Frank Verstraete
2. S. White
3. M. Fishman
4. E. Stoudenmire
5. J. Haegeman
6. L. Vanderstraeten

In Statistical and Nonlinear Physics

1. E. Stoudenmire
2. S. White
3. M. Fishman
4. J. Haegeman
5. L. Vanderstraeten
6. Frank Verstraete
7. Andrew J. Daley
8. Ulrich Schollwoeck

Citations in the corpus

• 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 [57] and fixed-point methods for computing PEPS environment tensors [58].”
• Tangent-space methods for uniform matrix product states (2018, background): “[83, 84] that aim to optimize the energy density in the thermodynamic limit directly.”