Flux insertion, entanglement, and quantized responses

TL;DR

This paper presents a method to construct ground states with flux insertion on finite rings using entanglement spectrum data, enabling the characterization of topological phases through quantized responses like Hall conductance.

Contribution

It introduces a novel approach linking entanglement spectrum quantum numbers to flux insertion, facilitating phase characterization and response calculations.

Findings

Successfully maps phase diagrams using Berry phase analysis.

Calculates Hall conductivity in quantum Hall systems.

Demonstrates the method's applicability to spin-1 models.

Abstract

We discuss the construction of a ground state wavefunction on a finite ring given the ground state on a long chain. In the presence of local symmetries, we can obtain the ground state with arbitrary flux inserted through the ring. A key ingredient are the quantum numbers of the entanglement spectrum. This method allows us to characterize phases by measuring quantized responses, such as the Hall conductance, using data contained in the entanglement spectrum. As concrete examples, we show how the Berry phase allows us to map out the phase diagram of a spin-1 model and calculate the Hall conductivity of a quantum Hall system.