  The Lee-Yang zeros are one-to-one mapping to zeros in the coherence of a
probe spin coupled to a many-body system. Here, we study the spin squeezing
under two different types of Lee-Yang dephasing channels in which the partition
functions vanish at Lee-Yang zeros. Under the first type of the channels in
which probes are coupled to their own bath, we find that the performance of
spin squeezing is improved and its maximum only depends on the initial state.
Moreover, the centers of all the concurrence vanishing domains are
corresponding to the Lee-Yang zeros. Under the second type of the channels in
which probes are coupled to one bath together, the performance of spin
squeezing is not improved, however, the concurrence shares almost the same
properties under both channels. These results provide new experimental
possibilities in many-body physics and extend a new perspective of the
relationship between the entanglement and spin squeezing in probes-bath
systems.
