Highly Entangled 2D Ground States: Tensor Network, Order Parameter and Correlation

TL;DR

This paper provides analytical tensor network representations and correlation analyses for 2D ground states exhibiting quantum phase transitions, revealing new insights into entanglement and phase behavior.

Contribution

It introduces exact tensor network constructions for 2D ground states with phase transitions, extending holographic networks and analyzing correlation functions.

Findings

Tensor networks for 2D ground states are constructed explicitly.

Correlation functions reveal exotic phase transition characteristics.

Entanglement entropy scales from area law to volume law.

Abstract

In this article we present analytical results on the exact tensor network representations and correlation functions of the first examples of 2D ground states with quantum phase transitions between area law and extensive entanglement entropy. The tensor networks constructed are one dimension higher than the lattices of the physical systems, allowing entangled physical degrees of freedoms to be paired with one another arbitrarily far away. Contraction rules of the internal legs are specified by a simple translationally invariant set of rules in terms of the tesselation of cubes or prisms in 3D space. The networks directly generalize the previous holographic tensor networks for 1D Fredkin and Motzkin chains. We also analyze the correlation in the spin and color sectors from the scaling of the height function of random surfaces, revealing additional characterizations of the exotic phase transitions.