# Isometric Tensor Network States in Two Dimensions

## TL;DR

This paper introduces an isometric tensor network state approach for 2D quantum systems, enabling efficient contraction and simulation of ground states, demonstrated on the 2D transverse field Ising model.

## Contribution

The paper presents a novel isometric restriction of tensor network states for 2D systems, improving contraction efficiency and enabling new algorithms like TEBD$^2$ for ground state approximation.

## Key findings

- Efficient contraction of 2D isometric tensor network states.
- Transformation of 2D quantum states into isometric TNS.
- Successful application of TEBD$^2$ to the 2D transverse field Ising model.

## Abstract

Tensor network states (TNS) are a promising but numerically challenging tool for simulating two-dimensional (2D) quantum many-body problems. We introduce an isometric restriction of the TNS ansatz that allows for highly efficient contraction of the network. We consider two concrete applications using this ansatz. First, we show that a matrix-product state representation of a 2D quantum state can be iteratively transformed into an isometric 2D TNS. Second, we introduce a 2D version of the time-evolving block decimation algorithm (TEBD$^2$) for approximating the ground state of a Hamiltonian as an isometric TNS, which we demonstrate for the 2D transverse field Ising model.