Reduced Contraction Costs of Corner-Transfer Methods for PEPS

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 $\mathcal{O}({\chi }^3{D}^6)$ to $\mathcal{O}({\chi }^3{D}^3)$ 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.

7 pages, 9 figures