Abstract
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 T_A of subsystem A is not a parameter but can be determined from the entanglement von Neumann entropy S_A and the total energy E_A of subsystem A calculated for the ground state of the whole system. We show that temperature 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 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 S_A and the total energy 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 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.