Eur. Phys. J. Plus (2022) 137: 229
https://doi.org/10.1140/epjp/s13360-022-02448-6

Regular Article

Bipartite entanglement and quantum correlation and phase transition in quantum wires under Tomonaga-Luttinger liquid: spinon and holon modes analysis

Department of Physics, K. N. Toosi University of Technology, 15875-4416, Tehran, Iran

^a afzali@kntu.ac.ir

Received: 20 July 2021
Accepted: 4 February 2022
Published online: 15 February 2022

Abstract

We investigate quantum correlation of quantum wires under Tomonaga-Luttinger Liquid (TLL) model via examining concurrence and quantum discord at zero temperature in terms of the coupling parameters, the velocity and the relative distance of the fermions. Using two-particle Green’s function of TLL model, we obtain the two-fermion spin-space density matrix (Werner state) for both spinless and spin-included cases. In the spin-included case, in which the TLL model consists of two collective excitation modes namely spinon and holon, under some circumstances, the concurrence has a constant value and is independent with respect to the coupling parameters. We show that the interaction of fermions with the same linearized dispersion does not effect on concurrence and also on quantum phase transition. Also, the convex of concurrence changes at a special distance of two fermions, and this result is the characteristic of the Tomonaga-Luttinger model. Furthermore, under the external potential, some of the coupling parameters can be changed, therefore, we can control quantum correlation of the system by changing the parameters.