Entanglement Entropy and Negativity in Inhomogeneous (1+1)D Systems: The Rainbow Chain, the SSD and their Holographic Dual

Starting with a system described by a conformal field theory (e.g. a critical spin chain or free fermions), one can find interesting violations to the typical logarithmic behavior of the bipartite entanglement entropy by introducing an inhomogeneous kinetic term in the Hamiltonian. Two examples of recent interest are the rainbow chain and the sine-squared deformed (SSD) model. Such systems can be equivalently described by placing the original CFT on a curved background manifold. Using the AdS/CFT correspondence, we develop a holographic dual description of inhomogeneous (1+1) dimensional systems by foliating the bulk spacetime with curved surfaces. Extending these foliations to the BTZ spacetime allows us to describe inhomogneous systems at finite temperatures. Using field-theoretic, holographic, and numerical techniques, we are able to compute the entanglement entropy and negativity, for various configurations of intervals, both at zero at finite temperatures, for the rainbow chain and the SSD.