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arXiv · 1903.03843

Conversion of projected entangled pair states into a canonical form

R. Haghshenas·Matthew J. O'Rourke·Garnet Kin-Lic Chan
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Abstract

We propose an algorithm to convert a projected entangled pair state (PEPS) into a canonical form, analogous to the well-known canonical form of a matrix product state. Our approach is based on a variational gauging ansatz for the QR tensor decomposition of PEPS columns into a matrix product operator and a finite depth circuit of unitaries and isometries. We describe a practical initialization scheme that leads to rapid convergence in the QR optimization. We explore the performance and stability of the variational gauging algorithm in norm calculations for the transverse-field Ising and Heisenberg models on a square lattice. We also demonstrate energy optimization within the PEPS canonical form for the transverse-field Ising and Heisenberg models. We expect this canonical form to open up improved analytical and numerical approaches for PEPS.

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R. Haghshenas, Matthew J. O'Rourke, Garnet Kin-Lic Chan. 2019-08-14. Conversion of projected entangled pair states into a canonical form. https://doi.org/10.1103/physrevb.100.054404

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