Entanglement entropy as an order parameter for strongly coupled nodal line semimetals

TL;DR

This paper demonstrates that entanglement entropy can serve as an effective non-local order parameter for topological quantum phase transitions in strongly coupled nodal line semimetals, revealing critical behavior and quantum correlations.

Contribution

It introduces a holographic model showing entanglement entropy as a novel order parameter for TQPTs in NLSMs, extending quantum information tools to topological phase transitions.

Findings

Entanglement entropy acts as an order parameter for TQPT in NLSMs.

Derivative of EE diverges at the critical point, indicating phase transition.

Quantum correlations are characterized across the quantum critical region.

Abstract

Topological semimetals are a class of many-body systems exhibiting novel macroscopic quantum phenomena at the interplay between high energy and condensed matter physics. They display a topological quantum phase transition (TQPT) which evades the standard Landau paradigm. In the case of Weyl semimetals, the anomalous Hall effect is a good non-local order parameter for the TQPT, as it is proportional to the separation between the Weyl nodes in momentum space. On the contrary, for nodal line semimetals (NLSM), the quest for an order parameter is still open. By taking advantage of a recently proposed holographic model for strongly-coupled NLSM, we explicitly show that entanglement entropy (EE) provides an optimal probe for nodal topology. We propose a generalized $c$-function, constructed from the EE, as an order parameter for the TQPT. Moreover, we find that the derivative of the renormalized EE with respect to the external coupling driving the TQPT diverges at the critical point, signaling the rise of non-local quantum correlations. Finally, we show that these quantum information quantities might be able to characterize not only the critical point but the whole quantum critical region at finite temperature.