Scaling of entanglement in $2+1$-dimensional scale-invariant field theories

Abstract

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-one-dimensional 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.

Mildly revised version; 11 pages, 8 figures (one mildly edited figure) and 73 references (six new references)

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Cited by in corpus (9)

• Topological order and criticality in (2+1)D monitored random quantum circuits
• Quantum criticality in the nonunitary dynamics of $(2+1)$-dimensional free fermions
• Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory
• Entanglement entropy from non-equilibrium Monte Carlo simulations
• Universal signatures of Dirac fermions in entanglement and charge fluctuations
• Holographic torus entanglement and its RG flow
• Structured volume-law entanglement in an interacting, monitored Majorana spin liquid
• Shape dependence of two-cylinder Renyi entropies for free bosons on a lattice
• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling