  The quantum phase transition (QPT) of the one-dimensional (1D) quantum
compass model in a transverse magnetic field is studied in this paper. An exact
solution is obtained by using an extended Jordan and Wigner transformation to
the pseudo-spin operators. The fidelity susceptibility, the concurrence, the
block-block entanglement entropy, and the pseudo-spin correlation functions are
calculated with antiperiodic boundary conditions. The QPT driven by the
transverse field only emerges at zero field and is of the second-order. Several
critical exponents obtained by finite size scaling analysis are the same as
those in the 1D transverse field Ising model, suggesting the same universality
class. A logarithmic divergence of the entanglement entropy of a block at the
quantum critical point is also observed. From the calculated coefficient
connected to the central charge of the conformal field theory, it is suggested
that the block entanglement depends crucially on the detailed topological
structure of a system.
