Code CFTs and Topological Matter

TL;DR

This paper introduces a new framework using code-based Narain conformal field theories to model topological phases of matter, revealing emergent topological features and fermionic excitations similar to known quantum Hall systems.

Contribution

It develops a novel code CFT construction based on Lie algebra lattices and demonstrates its ability to reproduce topological phenomena and fermionic excitations in lattice models.

Findings

Emergent topological features in code CFT models

Representation of code CFTs via Lie algebra lattices

Fermionic excitations with Dirac cones analogous to Haldane model

Abstract

In this paper, we propose a novel framework for modeling topological phases of matter using code-based Narain conformal field theories (NCFTs). We show that the algebraic structure of the NCFTs naturally embeds into critical lattice quantum field theory, yielding emergent topological features characteristic of gapless fermionic systems with non-zero Chern numbers. We develop a new representation of construction A of code CFT in terms of root and weight lattices of Lie algebras, focusing in particular on SU(2) and SU(3). We then derive the spectrum of particle states occupying the lattice and, with the help of fermionisation techniques, demonstrate that it hosts fermionic excitations with Dirac cones akin to tight binding systems namely the Haldane model of quantum anomalous hall effect on a honeycomb geometry.