Measuring topological entanglement entropy using Maxwell relations

TL;DR

This paper introduces a novel thermodynamic method to measure topological entanglement entropy in condensed matter systems by linking entropy changes in quantum point contacts to charge detection, enabling detection of topological order.

Contribution

It proposes a new protocol to measure TEE via Maxwell relations and charge detection, applicable to both Abelian and non-Abelian topological states.

Findings

Demonstrated the method for Abelian Laughlin states

Connected entropy change to charge detection in QPCs

Potential to detect non-Abelian topological states

Abstract

Topological entanglement entropy (TEE) is a key diagnostic of topological order, allowing to detect the presence of Abelian or non-Abelian anyons. However, there are currently no protocols to measure TEE in condensed matter systems. Here, we propose a scheme to measure the TEE, based on a nontrivial connection with the thermodynamic entropy change occurring in a quantum point contact (QPC) as it pinches off the topological liquid into two. We show how this entropy change can be extracted using Maxwell relations from charge detection of a nearby quantum dot. We demonstrate this explicitly for the Abelian Laughlin states, using an exact solution of the sine-Gordon model describing the universal crossover in the QPC. Our approach might open a new thermodynamic detection scheme of topological states also with non-Abelian statistics.