M-Body Pure State Entanglement

Abstract

The simple entanglement of N -body N -particle pure states is extended to the more general M -body or M -body N -particle states where N = M . Some new features of the M -body N -particle pure states are discussed. An application of the measure to quantify quantum correlations in a Bose-Einstien condensate model is demonstrated.

First order quantum phase transitions of the XX spin-1/2 chain in a uniform transverse field

“…[13] There are intimate links between QPTs and entanglement in the systems. [9,14−16] In this Letter it will be shown that there are a series of level-crossing points when the interaction strength and magnitude of the magnetic field satisfy certain conditions, and the entanglement measure [17,18] defined in terms of von Neumann entropy of one-body reduced density matrix can be used to indicating both the multi-particle entanglement and QPTs in the system.…”

“…if all N terms in the sum are non-zero, otherwise η(Ψ) = 0, where Ψ stands for the ground state wavefunction and (ρ Ψ ) i is the reduced density matrix with the i-th site only. It has been shown [18,22,23] that ( 7) is also suitable to measure genuine N -body entanglement. We observed that (ρ Ψ ) i is independent of i for the ground state in the model.…”

Exact diagonalization for spin-1/2 chains and the first order quantum phase transitions of the XXX chain in a uniform transverse field

“…Entanglement measure in the model is one of important quantities to characterize its QPT behavior, and is often studied by using block-block entanglement defined in terms of von Neumann entropy [15] by using Wootters concurrence [21] , e. g., that shown in [22]. In the following, we use the simple measure proposed in [17][18][19] with…”

“…if all N terms in the sum are non-zero, otherwise η(Ψ) = 0, where Ψ stands for the ground state wavefunction and (ρ Ψ ) i is the reduced density matrix with i-th spin-1 2 fermion only. It has been shown [17][18][19]23,24] that ( 6) is also suitable to measure genuine N -body entanglement in a quantum many-body system. We observed that (ρ Ψ ) i is i-independent for the ground state in the system for N even cases, while it becomes i-dependent for N odd cases.…”

Effect of Substrate Temperature on Epitaxial Orientation of Rh Thin Films Sputtered on A-Plane Sapphire

“…As an example, the code is applied to study XXX spin-1/2 chains with nearest neighbor interaction in a uniform transverse field, showing that there are a series of level-crossing points when the interaction strength and magnitude of the magnetic field satisfy certain conditions similar to the situation in the XX spin chain studied in [17]. The entanglement measure [18,19] defined in terms of the von Neumann entropy of one-body reduced density matrix is used to measure the multi-particle entanglement and reveal the QPTs in the system.…”