Swapping and permutation operators as entanglement witnesses for quantum Heisenberg spin-$s$ systems

Abstract

Using the SU($N$) representation of the group theory, we derive the general form of the spin swapping operator for the quantum Heisenberg spin-$s$ systems. We further prove that such a spin swapping operator is equal to the spin singlet pairing operator under the partial transposition. For SU(2) invariant states, it is shown that the expectation value of the spin swapping operator and its generalizations, the permutations, can be used as an entanglement witness, especially, for the formulation of observable conditions of entanglement.

8 pages, no figures, accepted by Journal of Physics A: Mathematical and General

References in corpus (17)

• Entanglement versus Correlations in Spin Systems
• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Entangled Quantum States of Magnetic Dipoles
• Entanglement in a second order quantum phase transition
• Entanglement Detection in the Stabilizer Formalism
• Entanglement Witnesses in Spin Models
• Entanglement in a Valence-Bond-Solid State
• Relations between Entanglement Witnesses and Bell Inequalities
• Energy as an Entanglement Witness for Quantum Many-Body Systems
• Entanglement Observables and Witnesses for Interacting Quantum Spin Systems
• Optimal Entanglement Witnesses for Qubits and Qutrits
• Boundary and impurity effects on entanglement of Heisenberg chains
• Entanglement in SO(3)-invariant bipartite quantum systems
• Entanglement in SU(2)-invariant quantum systems: The positive partial transpose criterion and others
• State space structure and entanglement of rotationally invariant spin systems
• Witnessing Entanglement with Second-Order Interference
• Stability of global entanglement in thermal states of spin chains

Cited by in corpus (11)

• Projective symmetry group classification of chiral spin liquids
• Paired chiral spin liquid with a Fermi surface in S=1 model on the triangular lattice
• Fermionic theory for quantum antiferromagnets with spin S > 1/2
• Bilinear Majorana representations for spin operators with spin magnitudes $S>1/2$
• From Entanglement Witness to Generalized Catalan Numbers
• Symmetry oscillations in strongly interacting one-dimensional mixtures
• Engineering of a Low-Entropy Quantum Simulator for Strongly Correlated Electrons Using SU($\mathcal{N}$)-Symmetric Cold Atom Mixtures
• Swapping Floquet time crystal
• Dynamical probing of high-order spin coherence in one-dimensional mixtures
• Matrix rearrangement approach for the entangling power with mixed qudit systems
• Symmetry oscillations sensitivity to SU(2)-symmetry breaking in quantum mixtures