Entanglement transitions in random definite particle states
Vikram S. Vijayaraghavan, Udaysinh T. Bhosale, Arul Lakshminarayan · Physical Review A · 2011
Entanglements within qubits are studied for the subspace of definite particle states or definite number of up spins. A transition from an algebraic decay of entanglement within two qubits with the total number $N$ of qubits to an exponential one when the number of particles is increased from two to three is studied in detail. In particular the probability that the concurrence is nonzero is calculated using statistical methods and is shown to agree with numerical simulations. Further entanglement within a block of $m$ qubits is studied using the log-negativity measure, which indicates that a transition from algebraic to exponential decay occurs when the number of particles exceeds $m$. Several algebraic exponents for the decay of the log negativity are analytically calculated. The transition is shown to be possibly connected to the changes in the density of states of the reduced density matrix, which has a divergence at the zero eigenvalue when the entanglement decays algebraically.