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Reduced Contraction Costs of Corner-Transfer Methods for PEPS
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abstract
We propose a pair of approximations that allows the leading order computational cost of contracting an infinite projected entangled-pair state (iPEPS) to be reduced from $\mathcal{O}(\chi^3D^6)$ to $\mathcal{O}(\chi^3D^3)$ when using a corner-transfer approach. The first approximation involves (i) reducing the environment needed for truncation of the boundary tensors (ii) relies on the sequential contraction and truncation of bra and ket indices, rather than doing both together as with the established algorithm. To verify the algorithm, we perform benchmark simulations over square lattice Heisenberg model and obtain results that are comparable to the standard iPEPS algorithm. The improvement in computational cost enables us to perform large bond dimension calculations, extending its potential to solve challenging problems.
Forward citations
Cited by 2 Pith papers
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Fast two-dimensional tensor-network contraction via subspace iteration
A new CTMRG variant, SI-CTMRG, substitutes QR-based subspace iteration for the dominant large SVD, shifting cost to tensor contractions and enabling state-of-the-art iPEPS calculations on a single H100 GPU.
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Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach
Split-CTMRG, which keeps the bra and ket layers of an infinite PEPS network separate and renormalizes them independently, reduces contraction cost and enables variational optimization at bond dimension 10 with retaine...
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