Fidelity mechanics, a scheme to investigate critical phenomena in quantum many-body physics, is formulated as an analogue of four laws in thermodynamics and black hole mechanics, thus unveiling a formal connection between critical points and black holes.

Rich physics is unveiled even for simple, or say, prototypical models in quantum many-body systems, such as the one-dimensional quantum XY model and the quantum transverse Ising chain in a longitudinal field. This enables us to clarify a confusing point for the so-called long-range entanglement driven order. The latter is believed to be present in the disordered regime for the quantum XY chain.