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

• Published in: The journal of high energy physics Vol. 2023; no. 5; pp. 221 - 33
• Main Authors: Baggioli, Matteo, Liu, Yan, Wu, Xin-Meng
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 29-05-2023; Springer Nature B.V; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Condensed matter physics; Critical point; Elementary Particles; Entropy; Gauge-Gravity Correspondence; Hall effect; High energy physics; Holography and Condensed Matter Physics (AdS/CMT); Metalloids; Order parameters; Phase transitions; Physics; Physics and Astronomy; Quantum entanglement; Quantum Field Theories; Quantum Field Theory; Quantum phenomena; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Topology; Gauge-Gravity Correspondence; Holography and Condensed Matter Physics (AdS/CMT)
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2023)221

A
bstract
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 are able to characterize not only the critical point but also features of the quantum critical region at finite temperature.