Quantum Quench dynamics in XY spin chain with ferromagnetic and antiferromagnetic interactions

TL;DR

This paper explores the phase diagram and dynamic critical behaviors of the one-dimensional XY spin chain with ferromagnetic and antiferromagnetic interactions, revealing new insights into entanglement oscillations and phase transitions.

Contribution

It introduces a quantum renormalization-group analysis of the XY model with mixed interactions, identifying three phases and proposing entanglement oscillation periods as a new order parameter.

Findings

Identification of three distinct phases in the model.

Oscillatory behavior of entanglement concurrence over time.

Proposal of oscillation period as a new order parameter for quantum phase transitions.

Abstract

In this manuscript we investigate the one-dimensional anisotropic XY model with ferromagnetic and antiferromagnetic interactions, which gives more interesting phase diagrams and dynamic critical behaviors. By using quantum renormalization-group method, we find that there are three phases in the system: antiferromagnetic Ising phase ordered in "x direction", spin-fluid phase and ferromagnetic Ising phase ordered in "y direction". In order to study the dynamical critical behaviors of the system, two quantum quenching methods are used. In both cases, the concurrence, a measure of entanglement, oscillates periodically over time. We show that the periods are the same and can be used as a new order parameter for quantum phase transitions. For further discussion, we derive the scaling exponent, {\theta}, and correlation length exponent, {\nu}, from the scaling behavior of the evolution period.