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Quantum Studies Mathematics and Foundations

The Hilbert–Schmidt norm as a measure of entanglement in spin-1/2 Heisenberg chain: generalized Bell inequality and distance between states

Saulo Luis Lima da Silva, Daniel H. T. Franco

Published Jan 23, 2022• 1 citation
Publisher
DOI
10.1007/s40509-021-00266-6

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Thermal entanglement in 2⊗32\otimes32⊗3 Heisenberg chains via distance between states
Most of the work involving entanglement measurement focuses on systems that can be modeled by two interacting qubits. This is due to the fact that there are few studies presenting entanglement analytical calculations in systems with spins s>1/2s > 1/2s>1/2. In this paper we present for the first time an analytical way of calculating thermal entanglement in a dimension 2⊗32\otimes32⊗3 Heisenberg chain through the distance between states. We use the Hilbert-Schmidt norm to obtain entanglement. The result obtained can be used to calculate entanglement in chains with spin-1/21/21/2 coupling with spin-111, such as ferrimagnetic compounds as well as compounds with dimer-trimer coupling.
The quantum entanglement measure is determined, for the first time, for a collection of spin-1/2 arranged in a infinite chain with finite temperature and applied to a single-crystal β-\mathrm{T_eVO_4}. The physical quantity proposed here to measure the entanglement is the distance between states by adopting the Hilbert-Schmidt norm. We relate the distance between states with the magnetic susceptibility. The decoherence temperature, above which the entanglement is suppressed, is determined for a system. A correlation among their decoherence temperatures and their respective exchange coupling constants is established, moreover, it is conjectured that the exchange coupling protects the system from decoherence as temperature increases.