Wavefunctions of Symmetry Protected Topological Phases from Conformal Field Theories

TL;DR

This paper introduces a novel method connecting 2D symmetry protected topological wavefunctions with conformal field theories, revealing deep links between microscopic models, critical theories, and entanglement properties.

Contribution

It generalizes the CFT approach for SPTs, establishing a framework to analyze wavefunctions, entanglement spectra, and responses to symmetry fluxes using conformal field theories.

Findings

CFT description emerges at large scale for various SPT wavefunctions

Existence of hidden quasi-long-range order in many SPTs proven via plasma analogy

Bulk and entanglement spectrum CFTs often coincide, but not always

Abstract

We propose a method for analyzing two-dimensional symmetry protected topological (SPT) wavefunctions using a correspondence with conformal field theories (CFTs) and integrable lattice models. This method generalizes the CFT approach for the fractional quantum Hall effect wherein the wavefunction amplitude is written as a many-operator correlator in the CFT. Adopting a bottom-up approach, we start from various known microscopic wavefunctions of SPTs with discrete symmetries and show how the CFT description emerges at large scale, thereby revealing a deep connection between group cocyles and critical, sometimes integrable, models. We show that the CFT describing the bulk wavefunction is often also the one describing the entanglement spectrum, but not always. Using a plasma analogy, we also prove the existence of hidden quasi-long-range order for a large class of SPTs. Finally, we show how response to symmetry fluxes is easily described in terms of the CFT.