BCS Effect on Quantum Correlation and Tripartite Quantum Entanglement in Spinless Gapless Tomonaga-Luttinger Liquid and Cuprate Superconducting Nanowire

It has been known that quantum information offers powerful instruments to investigate the properties of many-body systems. In this framework, we touched two particular aspect of this activity, namely the quantum entanglement and discord to compare the properties of gapless Tomonaga-Luttinger Liquid (TLL) model and the effect of BCS coupling in spinless fermions of TLL as a cuprate superconducting nanowire. Using two-fermion space-spin density matrix, we investigate quantum correlation of these cases via bipartite and tripartite entanglement, as well as quantum discord. The relations of concurrence (as a measure of quantum entanglement), the lower bound of the generalized robustness of tripartite entanglement and quantum discord in terms of the relative distance between fermions and the coupling parameter were accordingly obtained. The relationship between the compressibility as a physical property of system and quantum correlations has also been studied.