  We find that the first-order quantum phase transitions~(QPTs) are
characterized by intrinsic jumps of relevant operators while the continuous
ones are not. Based on such an observation, we propose a bond reversal method
where a quantity $\mathcal{D}$, the difference of bond strength~(DBS), is
introduced to judge whether a QPT is of first order or not. This method is
firstly applied to an exactly solvable spin-$1/2$ \textit{XXZ} Heisenberg chain
and a quantum Ising chain with longitudinal field where distinct jumps of
$\mathcal{D}$ appear at the first-order transition points for both cases. We
then use it to study the topological QPT of a cross-coupled~($J_{\times}$) spin
ladder where the Haldane--rung-singlet transition switches from being
continuous to exhibiting a first-order character at $J_{\times, I} \simeq$
0.30(2). Finally, we study a recently proposed one-dimensional analogy of
deconfined quantum critical point connecting two ordered phases in a spin-$1/2$
chain. We rule out the possibility of weakly first-order QPT because the DBS is
smooth when crossing the transition point. Moreover, we affirm that such
transition belongs to the Gaussian universality class with the central charge
$c$ = 1.

Strongly Correlated Electrons;Statistical Mechanics