  By numerically exact calculations of spin-1/2 antiferromagnetic Heisenberg
models on small clusters, we demonstrate that quantum entanglement between
subsystems $A$ and $B$ in a pure ground state of a whole system $A+B$ can
induce thermal equilibrium in subsystem $A$. Here, the whole system is
bipartitoned with the entanglement cut that covers the entire volume of
subsystem $A$. Temperature ${\cal T}_{A}$ of subsystem $A$ is not a parameter
but can be determined from the entanglement von Neumann entropy ${\cal S}_{A}$
and the total energy ${\cal E}_{A}$ of subsystem $A$ calculated for the ground
state of the whole system. We show that temperature ${\cal T}_{A}$ can be
derived by minimizing the relative entropy for the reduced density matrix
operator of subsystem $A$ and the Gibbs state (i.e., thermodynamic density
matrix operator) of subsystem $A$ with respect to the coupling strength between
subsystems $A$ and $B$. Temperature ${\cal T}_{A}$ is essentially identical to
the thermodynamic temperature, for which the entropy and the internal energy
evaluated using the canonical ensemble in statistical mechanics for the
isolated subsystem $A$ agree numerically with the entanglement entropy ${\cal
S}_{A}$ and the total energy ${\cal E}_{A}$ of subsystem $A$.Fidelity
calculations ascertain that the reduced density matrix operator of subsystem
$A$ for the pure but entangled ground state of the whole system $A+B$ matches,
within a maximally $1.5\%$ error in the finite size clusters studied, the
thermodynamic density matrix operator of subsystem $A$ at temperature ${\cal
T}_{A}$. We argue that quantum fluctuation in an entangled pure state can mimic
thermal fluctuation in a subsystem. We also provide two simple but nontrivial
analytical examples of free bosons and free fermions for which these statements
are exact. We furthermore discuss implications and possible applications of our
finding.
