It is generally believed that in spatial dimension d Ͼ 1, the leading contribution to the entanglement entropy S =−tr A log A scales as the area of the boundary of subsystem A. The coefficient of this "area law" is nonuniversal. However, in the neighborhood of a quantum critical point S is believed to possess subleading universal corrections. In the present work, we study the entanglement entropy in the quantum O͑N͒ model in 1 Ͻ d Ͻ 3. We use an expansion in ⑀ =3−d to evaluate ͑i͒ the universal geometric correction to S for an infinite cylinder divided along a circular boundary; ͑ii͒ the universal correction to S due to a finite correlation length. Both corrections are different at the Wilson-Fisher and Gaussian fixed points, and the ⑀ → 0 limit of the Wilson-Fisher fixed point is distinct from the Gaussian fixed point. In addition, we compute the correlation length correction to the Renyi entropy S n = 1 1−n log tr A n in ⑀ and large-N expansions. For N → ϱ, this correction generally scales as N 2 rather than the naively expected N. Moreover, the Renyi entropy has a phase transition as a function of n for d close to 3.

We develop a Hamiltonian picture for a family of models of nonrelativistic AdS/CFT duality. The Schrödinger group is realized via the conformal quantum mechanics of De Alfaro, Fubini and Furlan in the holographic direction. We show that most physical requirements, including the introduction of harmonic traps, can be realized with exact AdS metrics, but without any need for exotic matter sectors in the bulk dynamics. This Hamiltonian picture can be used to compare directly with many-body spectra of fermions at unitarity on harmonic traps, thereby providing a direct physical interpretation of the holographic radial coordinate for these systems. Finally, we add some speculations on the dynamical generation of mass gaps in the AdS description, the resulting quasiparticle spectra, and the analog of 'deconfining' phase transitions that may occur.