Infinite projected entangled pair states algorithm improved: Fast full update and gauge fixing

By Ho N. Phien, Johann A. Bengua, Hoang Duong Tuan, Philippe Corboz, Roman Orus. 2015

165 citations recorded by the source corpus.

The infinite projected entangled pair states (iPEPS) algorithm [J. Jordan et al., Phys. Rev. Lett. 101, 250602 (2008)] has become a useful tool in the calculation of ground-state properties of two-dimensional quantum lattice systems in the thermodynamic limit. Despite its many successful implementations, the method has some limitations in its present formulation which hinder its application to some highly entangled systems. The purpose of this paper is to unravel some of these issues, in turn enhancing the stability and efficiency of iPEPS methods. For this, we first introduce the fast full update scheme, where effective environment and iPEPS tensors are both simultaneously updated (or evolved) throughout time. As we shall show, this implies two crucial advantages: (i) dramatic computational savings and (ii) improved overall stability. In addition, we extend the application of the local gauge fixing, successfully implemented for finite-size PEPS [M. Lubasch et al., Phys. Rev. B 90, 064425 (2014)], to the iPEPS algorithm. We see that the gauge fixing not only further improves the stability of the method but also accelerates the convergence of the alternating least-squares sweeping in the (either ``full'' or ``fast full'') tensor update scheme. The improvement in terms of computational cost and stability of the resulting ``improved'' iPEPS algorithm is benchmarked by studying the ground-state properties of the quantum Heisenberg and transverse-field Ising models on an infinite square lattice.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/41523ffb644537a09295602c62a6d5db5fea7390

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

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Gradient methods for variational optimization of projected entangled-pair states (2016, methodology): “The model has been extensively studied with the PEPS ansatz [18,20,50], and we use the model as a benchmark for our conjugate-gradient method.”
Tangent-space methods for uniform matrix product states (2018, background): “This truncation can be done by a purely local singular-value decomposition – the so-called simple-update [80] algorithm – or by taking the full PEPS wavefunction into account – the full-update [81] or fast full-update algorithm [82].”
Stripe order in the underdoped region of the two-dimensional Hubbard model (2016, methodology): “In this work the optimization of the tensors has been done using an imaginary time evolution based on the so-called full update (58) (or fast-full update (59)), which is more accurate than the simple update approach (60).”