Ground states of unfrustrated spin Hamiltonians satisfy an area law

TL;DR

This paper proves that ground states of certain unfrustrated quantum spin systems obey an entanglement area law, enabling efficient descriptions and simulations of their ground spaces using tensor networks.

Contribution

It establishes an area law for ground states of unfrustrated spin-1/2 systems with entangled excited states and introduces an efficient tensor network representation for their ground spaces.

Findings

Ground states satisfy an entanglement area law.

Ground space can be efficiently represented by low-dimensional tensor networks.

Potential for efficient simulation of nearly frustration-free spin models.

Abstract

We show that ground states of unfrustrated quantum spin-1/2 systems on general lattices satisfy an entanglement area law, provided that the Hamiltonian can be decomposed into nearest-neighbor interaction terms which have entangled excited states. The ground state manifold can be efficiently described as the image of a low-dimensional subspace of low Schmidt measure, under an efficiently contractible tree-tensor network. This structure gives rise to the possibility of efficiently simulating the complete ground space (which is in general degenerate). We briefly discuss "non-generic" cases, including highly degenerate interactions with product eigenbases, using a relationship to percolation theory. We finally assess the possibility of using such tree tensor networks to simulate almost frustration-free spin models.