Finite-size corrections to entanglement in quantum critical systems

Abstract

We analyze the finite-size corrections to entanglement in quantum critical systems. By using conformal symmetry and density functional theory, we discuss the structure of the finite-size contributions to a general measure of ground state entanglement, which are ruled by the central charge of the underlying conformal field theory. More generally, we show that all conformal towers formed by an infinite number of excited states (as the size of the system $L\ensuremath{\rightarrow}\ensuremath{\infty}$) exhibit a unique pattern of entanglement, which differ only at leading order ${(1∕L)}^{2}$. In this case, entanglement is also shown to obey a universal structure, given by the anomalous dimensions of the primary operators of the theory. As an illustration, we discuss the behavior of pairwise entanglement for the eigenspectrum of the spin-$1∕2$ $XXZ$ chain with an arbitrary length $L$ for both periodic and twisted boundary conditions.