  We use an alternative method to investigate the quantum criticality at zero
and finite temperature using trace distance along with the density matrix
renormalization group. It is shown that the average correlation measured by the
trace distance between the system block and environment block in a DMRG sweep
is able to detect the critical points of quantum phase transitions at finite
temperature. As illustrative examples, we study spin-1 XXZ chains with uniaxial
single-ion-type anisotropy and the Heisenberg spin chain with staggered
coupling and external magnetic field. It is found that the trace distance shows
discontinuity at the critical points of quantum phase transition and can be
used as an indicator of QPTs.
