  Originating in questions regarding work extraction from quantum systems
coupled to a heat bath, quantum deficit, a kind of quantum correlations besides
entanglement and quantum discord, links quantum thermodynamics with quantum
correlations. In this paper, we evaluate the one-way deficit of two adjacent
spins in the bulk for the $XY$ model and its extend model: the extended Ising
model. We find that the one-way deficit susceptibility is able to characterize
the quantum phase transitions in the $XY$ model and even the topological phase
transitions in the extend Ising model. This study may enlighten extensive
studies of quantum phase transitions from the perspective of quantum
information processing and quantum computation, including finite-temperature
phase transitions, topological phase transitions and dynamical phase
transitions of a variety of quantum many-body systems.
