Entanglement and quantum-classical crossover in the extended XX model with long-range interactions

Abstract

In this work we considered the one-dimensional extended isotropic XY model (s=1/2) in a transverse field with uniform long-range interactions among the z components of the spins. We studied the classical critical behaviour of the model through the behaviour of the magnetization, isothermal susceptibility, internal energy and specific heat. We have obtained exact expressions for these functions and evaluated the critical exponents. The phase diagrams for the classical critical behaviour were built for three cases of the multiplicity p of the multiple spin interaction, namely p=2, p=3 and p→∞. We have also shown that the quantum phase transitions can also be characterized through two quantifiers of entanglement, namely, the concurrence and the von Neumann entropy. We have also verified through the von Neumann entropy how the central charge of the model is affected by the multiplicity p, the coupling exchange J2 and the uniform long-range interaction I.