String-net condensation: A physical mechanism for topological phases

TL;DR

This paper introduces string-net condensation as a fundamental physical mechanism for realizing topological phases, providing exactly soluble models and revealing the emergence of gauge bosons and fermions in higher dimensions.

Contribution

It develops exactly solvable Hamiltonians for string-net condensed states, linking topological phases to tensor category theory and demonstrating emergent particles in 3D models.

Findings

Exactly soluble 2D models for topological phases

Realization of fault-tolerant quantum computing models

Emergence of gauge bosons and fermions in 3D

Abstract

We show that quantum systems of extended objects naturally give rise to a large class of exotic phases - namely topological phases. These phases occur when the extended objects, called ``string-nets'', become highly fluctuating and condense. We derive exactly soluble Hamiltonians for 2D local bosonic models whose ground states are string-net condensed states. Those ground states correspond to 2D parity invariant topological phases. These models reveal the mathematical framework underlying topological phases: tensor category theory. One of the Hamiltonians - a spin-1/2 system on the honeycomb lattice - is a simple theoretical realization of a fault tolerant quantum computer. The higher dimensional case also yields an interesting result: we find that 3D string-net condensation naturally gives rise to both emergent gauge bosons and emergent fermions. Thus, string-net condensation provides a mechanism for unifying gauge bosons and fermions in 3 and higher dimensions.