Probing the conformal Calabrese-Cardy scaling with cold atoms

Abstract

We demonstrate that current experiments using cold bosonic atoms trapped in one-dimensional optical lattices and designed to measure the second-order R\'enyi entanglement entropy ${S}_{2}$ can be used to verify detailed predictions of conformal field theory (CFT) and estimate the central charge $c$. We discuss the adiabatic preparation of the ground state at half filling and small hopping parameter $J/U$, where we expect a CFT with $c=1$. We provide two complementary methods to estimate and subtract the classical entropy generated by the experimental preparation and imaging processes. We compare numerical calculations for the classical O(2) model with a chemical potential on a ($1+1$)-dimensional lattice, and the quantum Bose-Hubbard Hamiltonian implemented in the experiments. ${S}_{2}$ is very similar for the two models and follows closely the Calabrese-Cardy scaling, $(c/8)ln({N}_{s})$, for ${N}_{s}$ sites with open boundary conditions, provided that the large subleading corrections are taken into account.