Investigation of the Behavior of Quantum Coherence in Quantum Phase Transitions of Two-Dimensional XY and Ising Models

TL;DR

This study explores how quantum coherence behaves near quantum phase transitions in 2D XY and Ising models, demonstrating that coherence can effectively detect critical points and determine critical exponents with less computational effort.

Contribution

It introduces a quantum renormalization group approach to analyze quantum coherence in 2D models, providing a simpler alternative to entanglement-based methods for identifying phase transitions.

Findings

Quantum coherence exhibits non-analytic behavior at critical points.

Scaling of the coherence derivative yields critical exponents.

Results align with entanglement analysis but require less computation.

Abstract

We investigate the behavior of quantum coherence of the ground states of 2D Heisenberg XY model and 2D Ising model with transverse field on square lattices, by using the method of Quantum Renormalization Group (QRG). We show that the non-analytic behavior of quantum coherence near the critical point, can detect quantum phase transition (QPT) of these models. We also use the scaling behavior of maximum derivative of quantum coherence, with system size, to find the critical exponent of coherence for both models and also the length exponent of the Ising model. The results are in close agreement with the ones obtained from entanglement analysis, that is while quantum coherence needs less computational calculations in comparison to entanglement approaches.