From Multipartite Entanglement to TQFT

TL;DR

This paper proposes a conjecture linking multipartite entanglement in gapped quantum phases to TQFT partition functions, and verifies it in (2+1)-dimensional models, suggesting a deep connection between entanglement and topological order.

Contribution

It introduces a conjecture relating multipartite entanglement to TQFT partition functions and verifies it in specific (2+1)D models, advancing understanding of topological phases.

Findings

Conjecture relates ground state entanglement to TQFT partition functions.

Verification of the conjecture in (2+1)-dimensional Levin-Wen models.

Ground state wavefunction determines the modular tensor category.

Abstract

At long distances, a gapped phase of matter is described by a topological quantum field theory (TQFT). We conjecture a tight and concrete relationship between the genuine $(d+1)$-partite entanglement -- labelled by a $d$-dimensional manifold $M$ -- in the ground state of a $(d-1)+1$-dimensional gapped theory and the partition function of the low energy TQFT on $M$. In particular, the conjecture implies that for $d=3$, the ground state wavefunction can determine the modular tensor category description of the low energy TQFT. We verify our conjecture for general (2+1)-dimensional Levin-Wen string-net models.