Studies in Spin Systems.

One- (1D) and two-dimensional (2D) quantum-spin systems with additional spins are studied with the exact diagonalization method. The 2D system has a close relation with the high- ${\mathit{T}}_{\mathit{c}}$ superconductors, according to the model suggested by one of the authors. Since the transfer energy is taken to be 0 here, the model treated here is reduced to a ``doped'' Heisenberg antiferromagnet. The creation of spin polarons by the introduction of additional spins is observed in both 1D and 2D systems. Moreover, when two additional spins are doped on different sublattices, the spin state becomes similar to that of the antiferromagnet without additional spins. The interaction between additional spins is obtained as a function of the distance between them and is found to be attractive. It is short ranged in the 1D system while it is long ranged in the 2D system, reflecting the character of the background spin systems.One- (1D) and two-dimensional (2D) quantum-spin systems with additional spins are studied with the exact diagonalization method. The 2D system has a close relation with the high-${\mathit{T}}_{\mathit{c}}$ superconductors, according to the model suggested by one of the authors. Since the transfer energy is taken to be 0 here, the model treated here is reduced to a ``doped'' Heisenberg antiferromagnet. The creation of spin polarons by the introduction of additional spins is observed in both 1D and 2D systems. Moreover, when two additional spins are doped on different sublattices, the spin state becomes similar to that of the antiferromagnet without additional spins. The interaction between additional spins is obtained as a function of the distance between them and is found to be attractive. It is short ranged in the 1D system while it is long ranged in the 2D system, reflecting the character of the background spin systems.

Physical review. B, Condensed matterNov 1, 19904 citations

Spin Systems

WORLD SCIENTIFIC eBooksAug 20, 20180 citations

Studies of Exactly Solvable Spin Systems.

Man Mohan

Jan 1, 19810 citations

Quantum-state tomography for spin- l systems

Holger Friedrich Hofmann, Shigeki Takeuchi

We show that the density matrix of a spin- $l$ system can be described entirely in terms of the measurement statistics of projective spin measurements along a minimum of $4l+1$ different spin directions. It is thus possible to represent the complete quantum statistics of any $N$ -level system within the spherically symmetric three-dimensional space defined by the spin vector. An explicit method for reconstructing the density matrix of a spin-1 system from the measurement statistics of five nonorthogonal spin directions is presented and the generalization to spin- $l$ systems is discussed.We show that the density matrix of a spin-$l$ system can be described entirely in terms of the measurement statistics of projective spin measurements along a minimum of $4l+1$ different spin directions. It is thus possible to represent the complete quantum statistics of any $N$-level system within the spherically symmetric three-dimensional space defined by the spin vector. An explicit method for reconstructing the density matrix of a spin-1 system from the measurement statistics of five nonorthogonal spin directions is presented and the generalization to spin-$l$ systems is discussed.

arXiv:quant-ph/0310003Physical Review AApr 23, 200436 citations

Two Studies of One-Dimensional Spin Systems.

James D. Johnson

Jan 1, 19720 citations

Spin entanglement and nonlocality of multifermion systems

M. R. Arifullin, Vitaly L. Berdinskiy

Spin density matrices of the system, containing arbitrary even number N of indistinguishable fermions with spin S = 1/2, described by antisymmetric wave function, have been calculated. The indistinguishability and the Pauli principles are proved to determine uniquely spin states, spin correlations and entanglement of fermion spin states. Increase of the particle number in the multifermion system reduces the spin correlation in any pair of fermions. The fully entangled system of N electrons are shown to be composed by pairs with nonentangled spin states that is the incoherent superposition of the singlet and triplet states. Any large system of N fermions, such as electrons with spin S = 1/2, the spin state of any particle are shown to be entangled with the other part of the system containing N-1 particle. However, the spin state of this electron is not entangled with any other particle, and spin state of any electron pair is not entangled. These properties of spin states manifest in the Einstein-Podolsky-Rosen as confirmation or violation of the Bell inequalities indicating the presence of non-local quantum spin correlations.Spin density matrices of the system, containing arbitrary even number N of indistinguishable fermions with spin S = 1/2, described by antisymmetric wave function, have been calculated. The indistinguishability and the Pauli principles are proved to determine uniquely spin states, spin correlations and entanglement of fermion spin states. Increase of the particle number in the multifermion system reduces the spin correlation in any pair of fermions. The fully entangled system of N electrons are shown to be composed by pairs with nonentangled spin states that is the incoherent superposition of the singlet and triplet states. Any large system of N fermions, such as electrons with spin S = 1/2, the spin state of any particle are shown to be entangled with the other part of the system containing N-1 particle. However, the spin state of this electron is not entangled with any other particle, and spin state of any electron pair is not entangled. These properties of spin states manifest in the Einstein-Podolsky-Rosen as confirmation or violation of the Bell inequalities indicating the presence of non-local quantum spin correlations.

arXiv:1310.2863Oct 10, 20130 citations

One- (1D) and two-dimensional (2D) quantum-spin systems with additional spins are studied with the exact diagonalization method. The 2D system has a close relation with the high-

{\mathit{T}}_{\mathit{c}}

superconductors, according to the model suggested by one of the authors. Since the transfer energy is taken to be 0 here, the model treated here is reduced to a ``doped'' Heisenberg antiferromagnet. The creation of spin polarons by the introduction of additional spins is observed in both 1D and 2D systems. Moreover, when two additional spins are doped on different sublattices, the spin state becomes similar to that of the antiferromagnet without additional spins. The interaction between additional spins is obtained as a function of the distance between them and is found to be attractive. It is short ranged in the 1D system while it is long ranged in the 2D system, reflecting the character of the background spin systems.

We show that the density matrix of a spin-

l

system can be described entirely in terms of the measurement statistics of projective spin measurements along a minimum of

4l+1

different spin directions. It is thus possible to represent the complete quantum statistics of any

N

-level system within the spherically symmetric three-dimensional space defined by the spin vector. An explicit method for reconstructing the density matrix of a spin-1 system from the measurement statistics of five nonorthogonal spin directions is presented and the generalization to spin-

l

systems is discussed.