2009/10/31 by R. Rossignoli, N. Canosa, J. M. Matera
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Condensed matter physics #Degenerate energy levels #Eigenvalues and eigenvectors #Ground state #Mathematical analysis #Mathematics #Parity (physics) #Physics #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Separable space #Spins #quant-ph
paper · pdf · doi:10.1103/physreva.80.062325
published as Physical Review A 80, 062325 (2009) · 6 pages, figures added
openalex publication_date 2009/12/10 · arxiv created 2009/12/11 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We determine the conditions for the existence of a pair of degenerate parity breaking separable eigenstates in general arrays of arbitrary spins connected through XYZ couplings of arbitrary range and placed in a transverse field, not necessarily uniform. Sufficient conditions under which they are ground states are also provided. It is then shown that in finite chains, the associated definite parity states, which represent the actual ground state in the immediate vicinity of separability, can exhibit entanglement between any two spins regardless of the coupling range or separation, with the reduced state of any two subsystems equivalent to that of pair of qubits in an entangled mixed state. The corresponding concurrences and negativities are exactly determined. The same properties persist in the mixture of both definite parity states. These effects become specially relevant in systems close to the XXZ limit. The possibility of field induced alternating separable solutions with controllable entanglement side limits is also discussed. Illustrative numerical results for the negativity between the first and the jth spin in an open spin s chain for different values of s and j are as well provided.