Finite-size scaling of the entanglement entropy of the quantum Ising chain withhomogeneous, periodically modulated and random couplings

Abstract

Using free-fermionic techniques we study the entanglement entropy of a block of contiguousspins in a large finite quantum Ising chain in a transverse field, with couplings of differenttypes: homogeneous, periodically modulated and random. We carry out a systematic studyof finite-size effects at the quantum critical point, and evaluate subleading corrections bothfor open and for periodic boundary conditions. For a block corresponding to a half of afinite chain, the position of the maximum of the entropy as a function of thecontrol parameter (e.g. the transverse field) can define the effective critical point inthe finite sample. On the basis of homogeneous chains, we demonstrate that thescaling behavior of the entropy near the quantum phase transition is in agreementwith the universality hypothesis, and calculate the shift of the effective criticalpoint, which has different scaling behaviors for open and for periodic boundaryconditions.