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Gradient methods for variational optimization of projected entangled-pair states

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arxiv 1606.09170 v2 pith:BMLJFRWL submitted 2016-06-29 cond-mat.str-el quant-ph

Laurens Vanderstraeten , Jutho Haegeman , Philippe Corboz , Frank Verstraete This is my paper
classification cond-mat.str-elquant-ph
keywords optimizationentangled-pairgradientmethodpepsprojectedstatesvariational
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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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. An Oracle-Free Quantum Algorithm for Nonadiabatic Quantum Molecular Dynamics

    quant-ph 2026-04 unverdicted novelty 6.0 of 10

    An oracle-free Trotter-based quantum algorithm for nonadiabatic molecular dynamics achieves circuit depth advantages over QROM architectures and retains T-gate scalability compared to quantum signal processing.

  2. SU(4) Heisenberg model on the hyperhoneycomb lattice

    cond-mat.str-el 2026-06 unverdicted novelty 5.0 of 10

    3D PEPS simulations of the SU(4) Heisenberg model on the hyperhoneycomb lattice extrapolate to a gapless spin-liquid ground state.

  3. SU(4) Heisenberg model on the hyperhoneycomb lattice

    cond-mat.str-el 2026-06 conditional novelty 5.0 of 10

    Numerical iPEPS with loop expansions indicates the SU(4) Heisenberg model on the hyperhoneycomb lattice has a gapless quantum spin-liquid ground state, consistent with prior variational Monte Carlo results.

  4. Les Houches Lecture Notes on Tensor Networks

    cond-mat.str-el 2025-12 unverdicted novelty 2.0 of 10

    A well-organized five-lecture review of tensor networks (MPS/PEPS/MPO) covering algorithms, phase classification, string-nets, strange correlators, and dualities; it contains no new research results.

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