On Freedman's lattice models for topological phases

TL;DR

This paper investigates Freedman's lattice models for topological phases on torus cellulations, providing numerical evidence that supports some aspects of the conjecture but also reveals discrepancies in the ground state space.

Contribution

The study offers numerical analysis of Freedman's models on torus, confirming parts of the conjecture and highlighting differences in the ground state structure.

Findings

Numerical data supports Freedman's conjecture.

The ground state space differs from the conjectured space.

Analysis is limited to the simplest nontrivial cases.

Abstract

Freedman proposes a family of Hamiltonians $H_{0,l}$ which define quantum loop gas models on any celluated compact surface. We study the simplest nontrivial cases: celluations of the torus. Our numerical data support Freedman's conjecture, but the conjectured space of ground states does not come out in full.