Narrow Results

The transmission of pure and mixed states along a quantum spin chain is investigated. Nonlocality between two qubits will evolve as it is transmitted through the quantum channel in a way that may violate or not the Clauser–Horne–Shimony–Holt (CHSH) Bell inequality at different times. This violation of local realism is analogue to the so-called sudden death and sudden birth features of entanglement. In the quantum channel, which will turn to be a damping one, some (mixed) states will be preferred according to the nature of the quantum correlations that are preserved during the evolution along the spin chain.

The Heisenberg spin 1/2 chain is revisited in the perturbative RG approach with special focus on the transition of the critical exponents. We give a compact review that first order RG in the couplings is sufficient to derive the exact transition from ν = 1 to ν = 2/3, if the boson radius obtained in the bosonization procedure is replaced by the exact radius obtained in the Bethe approach. We explain the fact, that from the bosonization procedure alone, the critical exponent can not be derived correctly in the isotropic limit J_z → J. We further state that this fact is important if we consider to bosonize the antiferromagnetic super spin chain for the quantum Hall effect.

The Heisenberg spin 1/2 chain is revisited in the perturbative RG approach with special focus on the transition of the critical exponents. We give a compact review that first order RG in the couplings is sufficient to derive the exact transition from ν = 1 to ν = 2/3, if the boson radius obtained in the bosonization procedure is replaced by the exact radius obtained in the Bethe approach. We explain the fact, that from the bosonization procedure alone, the critical exponent can not be derived correctly in the isotropic limit J_z → J. We further state that this fact is important if we consider to bosonize the antiferromagnetic super spin chain for the quantum Hall effect.