Beyond 1D: An Introduction to Tensor Networks in Two Dimensions

by Dr Nisa Ara (TIFR)

Thursday 16 Jul 2026, 11:30 → 12:30 Asia/Kolkata

A304 and on zoom

We discuss the key ideas that make two-dimensional tensor-network methods practical. We begin with infinite Projected Entangled Pair States (iPEPS), the natural two-dimensional generalization of MPS, and the optimization schemes used to variationally determine their ground states. We then address the central computational challenge of the method: the contraction of an infinite two-dimensional tensor network to evaluate physical observables. Two complementary approaches are presented. The first is the Corner Transfer Matrix Renormalization Group (CTMRG), which approximates the infinite environment surrounding a local tensor by iteratively renormalizing its boundary. The second is the Levin–Nave Tensor Renormalization Group (TRG), which instead coarse-grains the entire tensor network through successive local singular value decompositions. Together, these methods provide the essential computational machinery for studying strongly correlated quantum systems directly in the thermodynamic limit.