Diagonal Isometric Form for Tensor Product States in Two Dimensions

TL;DR

This paper introduces a new isometric tensor network form for two-dimensional tensor states, enabling efficient simulation of large quantum systems and their dynamics.

Contribution

It proposes an alternative isometric form for isoTPS with auxiliary tensors, improving the representation of entanglement in 2D tensor networks.

Findings

Efficiently captures entanglement in 2D area law states.

Accurately reproduces short-time dynamics at critical points.

Enables extension to various lattice geometries.

Abstract

Isometric tensor product states (isoTPS) generalize the isometric form of the one-dimensional matrix product states (MPS) to tensor networks in two and higher dimensions. Here, we introduce an alternative isometric form for isoTPS by incorporating auxiliary tensors to represent the orthogonality hypersurface. We implement the time evolving block decimation (TEBD) algorithm on this new isometric form and benchmark the method by computing ground states and the real time evolution of the transverse field Ising model in two dimensions on large square lattices of up to 1250 sites. Our results demonstrate that isoTPS can efficiently capture the entanglement structure of two-dimensional area law states. The short-time dynamics is also accurately reproduced even at the critical point. Our isoTPS formulation further allows for a natural extension to different lattice geometries, such as the honeycomb or kagome latice.