  The investigation of the first-order quantum phase transition (QPT) is far
from clarity in comparison to that of the second-order or continuous QPT, in
which the order parameter and associated broken symmetry can be clearly
identified and at the same time the concepts of universality class and critical
scaling can be characterized by critical exponents. Here we present a compared
study of these two kinds of QPT in the transverse Ising model. In the absence
of a longitudinal field, the ground state of the model exhibits a second-order
QPT from paramagnetic phase to ferromagnetic one, which is smeared out once the
longitudinal field is applied. Surprisingly, the first excited state involves a
first-order QPT as the longitudinal field increases, which has not been
reported in literature. Within the framework of a pattern picture we clearly
identify the difference between these two kinds of QPT: for the continuous QPT
only the pattern flavoring ferromagnetic phase is always dominant over the
others, and on the contrary, there exist at least two competitive patterns in
the first-order QPT, which is further indicated by patterns' occupancies
calculated by pattern projections on the ground and first excited states
wavefunctions. Our result has not only a fundamental significance in the
understandings of the nature of QPTs, but also a practical interest in quantum
simulations used to test the present finding.
