Entanglement transitions in random definite particle states

Abstract

Entanglement 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 non-zero is calculated using statistical methods and 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 with 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.

arXiv commentSubstantially added content (now 24 pages, 5 figures) with a discussion of the possible mechanism for the transition. One additional author in this version that is accepted for publication in Phys. Rev. A

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• Persistent entanglement in a class of eigenstates of quantum Heisenberg spin glasses
• Signatures of Integrability and Exactly Solvable Dynamics in an Infinite-Range Many-Body Floquet Spin System
• Exact Solvability Of Entanglement For Arbitrary Initial State in an Infinite-Range Floquet System