Algorithms for finite Projected Entangled Pair States

Abstract

Projected Entangled Pair States (PEPS) are a promising ansatz for the study of strongly correlated quantum many-body systems in two dimensions. But due to their high computational cost, developing and improving PEPS algorithms is necessary to make the ansatz widely usable in practice. Here we analyze several algorithmic aspects of the method. On the one hand, we quantify the connection between the correlation length of the PEPS and the accuracy of its approximate contraction, and discuss how purifications can be used in the latter. On the other, we present algorithmic improvements for the update of the tensor that introduce drastic gains in the numerical conditioning and the efficiency of the algorithms. Finally, the state-of-the-art general PEPS code is benchmarked with the Heisenberg and quantum Ising models on lattices of up to $21\times 21$ sites.

18 pages, 20 figures, accepted version

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• Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment
• Capturing exponential variance using polynomial resources: applying tensor networks to non-equilibrium stochastic processes
• Fermionic algebraic quantum spin liquid in an octa-kagome frustrated antiferromagnet
• Entanglement Hamiltonian of the quantum Néel state
• Infinite Matrix Product States vs Infinite Projected Entangled-Pair States on the Cylinder: a comparative study