Solving frustration-free spin systems

TL;DR

This paper identifies a broad class of frustration-free quantum spin systems that can be solved exactly using tensor networks, providing new insights into their ground states and entanglement properties.

Contribution

It introduces an exact solution method for frustration-free spin-1/2 models using tensor networks, and establishes an area law for their entanglement entropy.

Findings

Ground state manifold can be exactly constructed with tensor networks.

Models satisfy an area law for entanglement entropy.

Provides an efficient ansatz for simulating near frustration-free models.

Abstract

We identify a large class of quantum many-body systems that can be solved exactly: natural frustration-free spin-1/2 nearest-neighbor Hamiltonians on arbitrary lattices. We show that the entire ground state manifold of such models can be found exactly by a tensor network of isometries acting on a space locally isomorphic to the symmetric subspace. Thus, for this wide class of models real-space renormalization can be made exact. Our findings also imply that every such frustration-free spin model satisfies an area law for the entanglement entropy of the ground state, establishing a novel large class of models for which an area law is known. Finally, we show that our approach gives rise to an ansatz class useful for the simulation of almost frustration-free models in a simple fashion, outperforming mean field theory.