Entanglement and quantum phase transition in the one-dimensional anisotropic XY model

TL;DR

This paper investigates entanglement and quantum phase transitions in the one-dimensional anisotropic XY model using quantum renormalization group techniques, revealing fixed points, phase characteristics, and critical behaviors.

Contribution

It introduces a detailed analysis of entanglement and phase transitions in the XY model through renormalization, identifying fixed points and critical scaling behaviors.

Findings

Concurrence saturates at two distinct values for different phases.

Non-analytic behavior of the concurrence derivative at the critical point.

Scaling laws show divergence of the derivative with system size.

Abstract

In this paper the entanglement and quantum phase transition of the anisotropic s=1/2 XY model are studied by using the quantum renormalization group method. By solving the renormalization equations, we get the trivial fixed point and the untrivial fixed point which correspond to the phase of the system and the critical point, respectively. Then the concurrence between two blocks are calculated and it is found that when the number of the iterations of the renormalziation trends infinity, the concurrence develops two staturated values which are associated with two different phases, i.e., Ising-like and spin-fluid phases. We also investigate the first derivative of the concurrence, and find that there exists non-analytic behaviors at the quantum critical point, which directly associate with the divergence of the correlation length. Further insight, the scaling behaviors of the system are analyzed, it is shown that how the maximum value of the first derivative of the concurrence reaches the infinity and how the critical point is touched as the size of the system becomes large.