Diagonal entropy in many-body systems: Volume effect and quantum phase transitions

We investigate the diagonal entropy(DE) of the ground state for quantum many-body systems, including the XY model and the Ising model with next nearest neighbour interactions. We focus on the DE of a subsystem of L continuous spins. We show that the DE in many-body systems, regardless of integrability, can be represented as a volume term plus a logarithmic correction and a constant offset. Quantum phase transition points can be explicitly identified by the three coefficients thereof. Besides, by combining entanglement entropy and the relative entropy of quantum coherence, as two celebrated representatives of quantumness, we simply obtain the DE, which naturally has the potential to reveal the information of quantumness. More importantly, the DE is concerning only the diagonal form of the ground state reduced density matrix, making it feasible to measure in real experiments, and therefore it has immediate applications in demonstrating quantum supremacy on state-of-the-art quantum simulators.