Fig. 1: Entanglement entropy, area law, and the Gioev-Klich-Widom scaling.
From: Measuring entanglement entropy and its topological signature for phononic systems
a Entanglement entropy of subsystem A quantifies the entanglement or nonlocal correlation (depicted by the wavy line) between subsystem A and the remaining subsystem B. b Area law of the entanglement entropy emerges in gapped phases where the correlation length Îľ is much smaller than the other length scales. Thus, all the correlations between A and B are around the boundary of subsystem A within a region of thickness Îľ. c The Gioev-Klich-Widom law predicts a logarithmic scaling of entanglement entropy for gapless phases with a finite Fermi surface. d An emergent topological correspondence principle in the entanglement spectrum: the edge spectrum in the bulk band gap is connected to the entanglement spectrum by adiabatic principles. The inset illustrates the cutting of a cylinder surface (i.e., the 2D system with periodic boundary conditions along one direction) into two halves (A and B regions) to obtain the entanglement spectrum and entanglement entropy. The wavevector along the edge boundary is depicted by the green arrow.
