Skeleton of isometric Tensor Network States for Abelian String-Net Models

TL;DR

This paper introduces isometric tensor network states called skeletons for abelian topological order, enabling efficient classical computation and exploration of phase transitions beyond anyon condensation.

Contribution

The authors develop parametrized isometric tensor network states that connect topological phases and can be efficiently simulated classically, serving as a new tool for studying abelian topological order.

Findings

Stable finite correlation length deformations of string-net fixed points are constructed.

Expectation values of generalized Pauli strings can be efficiently computed classically.

Skeletons serve as an organizing principle and a testbed for quantum processors.

Abstract

We construct parametrized isometric tensor network states -- referred to as skeletons -- that allow us to explore phases of abelian topological order and can be efficiently implemented on quantum processors. We obtain stable finite correlation length deformations of string-net fixed points, which are constructed both by conserving virtual symmetries of the tensor and by imposing local isometry constraints. They connect distinct topological phases via a shared critical point, thereby providing analytically tractable examples of phase transitions beyond anyon condensation. By mapping such classes of 2D tensor networks to 1D stochastic automata with local update rules, we show that expectation values of generalized Pauli strings of arbitrary weight can be efficiently computed using classical methods. Therefore these skeletons not only serve as an organizing principle for abelian topological order but also provide a non-trivial testbed for quantum processors.