Entropic uncertainty relation and quantum phase transition in spin-1/2 Heisenberg chain

Based on the quantum-memory-assisted entropic uncertainty relation (QMA-EUR), we study the quantum phase transition (QPT) of a spin-1/2 frustrated Heisenberg chain and show that QMA entropy can be a useful tool to detect QPT. For the six-site case, we choose the reduced two-site as the detecting system and obtain the analytical result of QMA entropy and its bound. We find that the QMA entropy of the ground state is discontinuous at the first-order QPT point. Meanwhile for the excited state, the catastrophe point of QMA entropy approaches the infinite-order QPT point, which is confirmed by the numerical results in the 8-, 10- and 12-site cases. Moreover, we study the behavior of QMA entropy undergoing the dephasing process. Interestingly, two-site QMA entropy can still indicate the QPT point when the state degenerates into a mixed state. In this sense, QMA entropy is more effective than quantum correlation in reflecting the quantum criticality.