  The Lee-Yang theorem for the zeroes of the partition function is not strictly
applicable to quantum systems because the zeroes are defined in units of the
fugacity $e^{h\Delta\tau}$, and the Euclidean-time lattice spacing $\Delta\tau$
can be divergent in the infrared (IR). We recently presented analytic arguments
describing how a new space-Euclidean time zeroes expansion can be defined,
which reproduces Lee and Yang's scaling but avoids the unresolved branch points
associated with the breaking of nonlocal symmetries such as parity. We now
present a first numerical analysis for this new zeros approach for a quantum
spin chain system. We use our scheme to quantify the renormalization group flow
of the physical lattice couplings to the IR fixed point of this system. We
argue that the generic Finite-Size Scaling (FSS) function of our scheme is
identically the entanglement entropy of the lattice partition function and,
therefore, that we are able to directly extract the central charge, $c$, of the
quantum spin chain system using conformal predictions for the scaling of the
entanglement entropy.
