Tensor networks for frustrated systems: emergence of order from simplex entanglement

TL;DR

This paper introduces a novel tensor network framework based on triangular W-like simplices to describe the ground states of frustrated antiferromagnetic triangular lattices, revealing new insights into entanglement and order emergence.

Contribution

It proposes a new class of tensor networks using simplices instead of maximally entangled pairs, linking entanglement types to macroscopic order in frustrated systems.

Findings

Triangular W-like simplices represent degenerate ground states.

Antiferromagnetic frustration relates to W-states, contrasting ferromagnetic order from GHZ-like simplices.

Different simplices exhibit distinct entangling powers, influencing macroscopic order.

Abstract

We consider a frustrated anti-ferromagnetic triangular lattice Hamiltonian and show that the properties of the manifold of its degenerated ground state are represented by a novel type of tensor networks. These tensor networks are not based on ancillary maximally entangled pairs, but rather on triangular W-like simplices. Anti-ferromagnetic triangular frustration is then related to ancillary W-states in contrast to ferromagnetic order which emerges from the contraction of GHZ-like triangular simplices. We further discuss the outwards entangling power of various simplices. This analysis suggests the emergence of distinct macroscopic types of order from the classification of entanglement residing on the simplices that define a tensor network.