Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG

Abstract: We develop a QR-based corner transfer matrix renormalization group (CTMRG) framework for contracting infinite projected entangled-pair states (iPEPS) on honeycomb lattices. Our method explicitly uses the lattice's native C3v symmetry at each site, generalizing QR-based acceleration (previously limited to square lattices) to enable efficient and stable contractions. This approach achieves order-of-magnitude speedups over conventional singular value decomposition (SVD)-based CTMRG while maintaining high numerical precision. Comprehensive benchmark calculations for the spin-1/2 Heisenberg and Kitaev models demonstrate higher computational efficiency without sacrificing accuracy. We further employ our method to study the Kitaev-Heisenberg model, where we provide numerical evidence for the universal 1/r^4 decay of the dimer-dimer correlation function within the quantum spin liquid (QSL) phase. Our work establishes a framework for extending QR-based CTMRG to other lattice geometries, opening new avenues for studying exotic quantum phases with tensor networks.