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arXiv · 2411.12731

Finite-size scaling on the torus with periodic projected entangled-pair states

Gleb Fedorovich·Lukas Devos·Jutho Haegeman·Laurens Vanderstraeten·Frank Verstraete·Atsushi Ueda
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Abstract

An efficient algorithm is constructed for contracting two-dimensional tensor networks under periodic boundary conditions. The central ingredient is a novel renormalization step that scales linearly with system size, i.e. from $L \to L+1$. The numerical accuracy is comparable to state-of-the-art tensor network methods, while giving access to much more data points, and at a lower computational cost. Combining this contraction routine with the use of automatic differentiation, we arrive at an efficient algorithm for optimizing fully translation invariant projected entangled-pair states on the torus. Our benchmarks show that this method yields finite-size energy results that are comparable to those from quantum Monte Carlo simulations. When combined with field-theoretical scaling techniques, our approach enables accurate estimates of critical properties for two-dimensional quantum lattice systems.

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Gleb Fedorovich, Lukas Devos, Jutho Haegeman, Laurens Vanderstraeten, Frank Verstraete, Atsushi Ueda. 2024-11-19. Finite-size scaling on the torus with periodic projected entangled-pair states. https://doi.org/10.1103/physrevb.111.165124

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