2014/12/31 by Xiao Chen, Gil Young Cho, Thomas Faulkner +1 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal field theory #Dirac fermion #Entropy (arrow of time) #Fermion #Massless particle #Quadratic equation #Quantum Chromodynamics and Particle Interactions #Quantum entanglement #Quantum many-body systems #Scaling #Squashed entanglement #cond-mat.str-el #hep-th
paper · pdf · doi:10.1088/1742-5468/2015/02/p02010
published as Journal of Statitistical Mechanics, Vol. 2015, P02010 (2015) · Mildly revised version; 11 pages, 8 figures (one mildly edited figure) and 73 references (six new references)
arxiv created 2015/01/14 · openalex publication_date 2015/02/10 · arxiv updated 2015/02/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
We study the universal scaling behavior of the entanglement entropy of critical theories in 2 + 1 dimensions. We specially consider two fermionic scale-invariant models, free massless Dirac fermions and a model of fermions with quadratic band touching, and numerically study the two-cylinder entanglement entropy of the models on the torus. We find that in both cases the entanglement entropy satisfies the area law and has the subleading term which is a scaling function of the aspect ratios of the cylindrical regions. We test the scaling of entanglement in both the free fermion models using three possible scaling functions for the subleading term derived from (a) the quasi-1D conformal field theory, (b) the bosonic quantum Lifshitz model and (c) the holographic AdS/CFT correspondence. For the later case we construct an analytic scaling function using holography, appropriate for critical theories with a gravitational dual description. We find that the subleading term in the fermionic models is well described, for a range of aspect ratios, by the scaling form derived from the quantum Lifshitz model as well as that derived using the AdS/CFT correspondence (in this case only for the Dirac model). For the case where the fermionic models are placed on a square torus we find the fit to the different scaling forms is in agreement to surprisingly high precision.