  We investigate the relationship between two kinds of ground-state local
convertibility and quantum phase transitions in XY model. The local operations
and classical communications (LOCC) convertibility is examined by the
majorization relations and the entanglement-assisted local operations and
classical communications (E- LOCC) via Renyi entropy interception. In the phase
diagram of XY model, LOCC convertibility and ELOCC convertibility of
ground-states are presented and compared. It is shown that different phases in
the phase dia- gram of XY model can have different LOCC or ELOCC
convertibility, which can be used to detect the quantum phase transition. This
study will enlighten extensive studies of quantum phase transitions from the
perspective of local convertibility, e.g., finite-temperature phase transitions
and other quantum many-body models.

Quantum Physics