Exact entanglement renormalization for string-net models

TL;DR

This paper develops an exact renormalization group transformation for string-net models, providing a way to efficiently simulate and prepare their ground states using MERA and quantum circuits.

Contribution

It introduces an explicit RG transformation that preserves the fixed-point wave function and offers an exact MERA representation for string-net models.

Findings

Provides an explicit RG transformation for string-net models

Constructs an exact MERA representation of the ground state

Enables efficient numerical and quantum simulation of string-net states

Abstract

We construct an explicit renormalization group (RG) transformation for Levin and Wen's string-net models on a hexagonal lattice. The transformation leaves invariant the ground-state "fixed-point" wave function of the string-net condensed phase. Our construction also produces an exact representation of the wave function in terms of the multi-scale entanglement renormalization ansatz (MERA). This sets the stage for efficient numerical simulations of string-net models using MERA algorithms. It also provides an explicit quantum circuit to prepare the string-net ground-state wave function using a quantum computer.