Universal edge information from wave-function deformation

TL;DR

This paper demonstrates that all potential edge theories of a nonchiral topological phase can be derived solely from its fixed-point wave function through local deformations, without needing an underlying Hamiltonian.

Contribution

It introduces a method to extract all possible edge theories from the fixed-point wave function by local deformation, emphasizing a state-based approach to topological phases.

Findings

Edge theories can be obtained from deformed fixed-point wave functions.

Deformed wave functions reflect known edge theory types, including gapped and gapless.

Results do not depend on an underlying Hamiltonian, only on the quantum state.

Abstract

It is well known that the bulk physics of a topological phase constrains its possible edge physics through the bulk-edge correspondence. Therefore, the different types of edge theories that a topological phase can host constitute a universal piece of data which can be used to characterize topological order. In this paper, we argue that, beginning from only the fixed-point wave function (FPW) of a nonchiral topological phase and by locally deforming it, all possible edge theories can be extracted from its entanglement Hamiltonian (EH). We give a general argument, and concretely illustrate our claim by deforming the FPW of the Wen-plaquette model, the quantum double of $\mathbb{Z}_2$. In that case, we show that the possible EHs of the deformed FPW reflect the known possible types of edge theories, which are generically gapped, but gapless if translational symmetry is preserved. We stress that our results do not require an underlying Hamiltonian--thus, this lends support to the notion that a topological phase is indeed characterized by only a set of quantum states and can be studied through its FPWs.