Characterizing quantum phase transitions by the entanglement of high symmetric points: A quantum computational investigation

Quantum phase transitions play fundamental roles in our understanding of various properties of quantum materials. Therefore, how to characterize quantum phase transitions efficiently is pursued, especially for topological quantum phase transitions, which have no well-defined order parameters. Here we demonstrate that the entanglement of a small subset of a product state can be used as an indicator for quantum phase transitions. Moreover, this strategy can be easily applied with the near-term quantum computers, in which the number of qubits is highly limited. As examples, we demonstrate with IBM quantum computers for the transverse Ising and Kitaev spin model that the entanglement of product states formed by the states at the high-symmetric points of the Brillouin zone, which are subsets of the real ground state, can be used to determine different ground state phases.