  The {\it exchange} interaction arising from the particle indistinguishability
is of central importance to physics of many-particle quantum systems. Here we
study analytically the dynamical generation of quantum entanglement induced by
this interaction in an isolated system, namely, an ideal Fermi gas confined in
a chaotic cavity, which evolves unitarily from a non-Gaussian pure state. We
find that the breakdown of the quantum-classical correspondence of particle
motion, via dramatically changing the spatial structure of many-body
wavefunction, leads to profound changes of the entanglement structure.
Furthermore, for a class of initial states, such change leads to the approach
to thermal equilibrium everywhere in the cavity, with the well-known Ehrenfest
time in quantum chaos as the thermalization time. Specifically, the quantum
expectation values of various correlation functions at different spatial scales
are all determined by the Fermi-Dirac distribution. In addition, by using the
reduced density matrix (RDM) and the entanglement entropy (EE) as local probes,
we find that the gas inside a subsystem is at equilibrium with that outside,
and its thermal entropy is the EE, even though the whole system is in a pure
state. As a by-product of this work, we provide an analytical solution
supporting an important conjecture on thermalization, made and numerically
studied by Garrison and Grover in: Phys. Rev. X \textbf{8}, 021026 (2018), and
strengthen its statement.
