Scaling of bipartite entanglement in one-dimensional lattice systems with a trapping potential

We study the effects of a power-law trapping potential on the scaling behaviour of the entanglement at the quantum critical point of one-dimensional (1D) lattice particle systems. We compute bipartite von Neumann and Renyi entropies in the presence of the trap and analyse their scaling behaviour with increasing trap size. As a theoretical laboratory, we consider the quantum XY chain in an external transverse field acting as a trap for the spinless fermions of its quadratic Hamiltonian representation. We then investigate confined-particle systems described by the 1D Bose-Hubbard model in the superfluid phase ( around the centre of the trap). In both cases conformal field theory predicts logarithmically divergent bipartite entanglement entropies for the homogeneous systems without a trap. The presence of the trapping potential breaks conformal invariance, affecting the critical behaviour of the homogeneous system. Our results show that the bipartite entanglement entropies diverge logarithmically with increasing trap size and present notable scaling behaviours in the trap-size scaling limit.