Randomness of Eigenstates of Many-Body Quantum Systems.

The emergence of random eigenstates of quantum many-body systems in integrable-chaos transitions is the underlying mechanism of thermalization for these quantum systems. We use fidelity and modulus fidelity to measure the randomness of eigenstates in quantum many-body systems. Analytic results of modulus fidelity between random vectors are obtained to be a judge for the degree of randomness. Unlike fidelity, which just refers to a kind of criterion of necessity, modulus fidelity can measure the degree of randomness in eigenstates of a one-dimension (1D) hard-core boson system and identifies the integrable-chaos transition in this system.