  Recently, it was proposed that the chiral central charge of a gapped,
two-dimensional quantum many-body system is proportional to a bulk ground state
entanglement measure known as the modular commutator. While there is
significant evidence to support this relation, we show in this paper that it is
not universal. We give examples of lattice systems that have vanishing chiral
central charge which nevertheless give nonzero "spurious" values for the
modular commutator for arbitrarily large system sizes, in both one and two
dimensions. Our examples are based on cluster states and utilize the fact that
they can generate nonlocal modular Hamiltonians.
