Isometric Tensor Network representation of string-net liquids

TL;DR

This paper demonstrates that two-dimensional string-net liquids, representing many topological phases, can be exactly expressed as isometric tensor network states, showing the broad applicability of isoTNS in modeling complex quantum phases.

Contribution

It proves that 2D string-net liquids have an exact isoTNS representation and that this form can be maintained under finite depth local quantum circuits.

Findings

String-net liquids admit exact isoTNS representation

Isometric form preserved under finite depth local quantum circuits

Long-range entanglement does not prevent isoTNS representation

Abstract

Recently, a class of tensor networks called isometric tensor network states (isoTNS) was proposed which generalizes the canonical form of matrix product states to tensor networks in higher dimensions. While this ansatz allows for efficient numerical computations, it remained unclear which phases admit an isoTNS representation. In this work, we show that two-dimensional string-net liquids, which represent a wide variety of topological phases including discrete gauge theories, admit an exact isoTNS representation. We further show that the isometric form can be preserved after applying a finite depth local quantum circuit. Taken together, these results show that long-range entanglement by itself is not an obstruction to isoTNS representation and suggest that all two-dimensional gapped phases with gappable edges admit an isoTNS representation.