Entanglement Entropy with Background Gauge Fields

Abstract

We study the entanglement entropy, the Rényi entropy, and the mutual (Rényi) information of Dirac fermions on a 2 dimensional torus in the presence of constant gauge fields. We derive their general formulas using the equivalence between twisted boundary conditions and the background gauge fields. Novel and interesting physical consequences have been presented in arXiv:1705.01859. Here we provide detailed computations of the entropies and mutual information in a low temperature limit, a large radius limit, and a high temperature limit. The high temperature limit reveals rather different physical properties compared to those of the low temperature one: there exist two non-trivial limits that depend on a modulus parameter and are not smoothly connected.

37 pages, v2: some formulas in section 4.3 are corrected

References in corpus (5)

• Towards a derivation of holographic entanglement entropy
• Measuring entanglement entropy through the interference of quantum many-body twins
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
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Cited by in corpus (6)

• Thermodynamical property of entanglement entropy and deconfinement phase transition
• Aspects of quantum information in finite density field theory
• Holographic entanglement entropy of the double Wick rotated BTZ black hole
• Entanglement Entropy, Chemical Potential, Current Source, and Wilson Loop
• Entanglement entropy and Wilson loop
• QFT Entanglement Entropy, 2D Fermion and Gauge Fields