Quantum phase transition in the Dzyaloshinskii-Moriya interaction with inhomogeneous magnetic field: Geometric approach

TL;DR

This paper explores the relationship between entanglement, geometric phase, and quantum phase transitions in a Dzyaloshinskii-Moriya model under inhomogeneous magnetic fields, highlighting the roles of Berry phase and concurrence as indicators.

Contribution

It extends previous work to include nonuniform magnetic fields and analyzes the complementary roles of Berry phase and concurrence in detecting quantum phase transitions.

Findings

Berry phase is more suitable for small DM parameters

Concurrence is more suitable for large DM parameters

Berry phase and concurrence complement each other in phase transition detection

Abstract

In this paper, we generalize the results of S. Oh (Physics Letters A. 644-647 \textbf{373 }) to Dzyaloshinski-Moriya model under nonuniform external magnetic field to investigate the relation between entanglement, geometric phase (or Berry phase) and quantum phase transition. We use quaternionic representation to relate the geometric phase to the quantum phase transition. For small values of DM parameter, the Berry phase is more appropriate than the concurrence measure, while for large values, the concurrence is a good indicator to show the phase transition. On the other hand, by increasing the DM interaction the phase transition occurs for large values of anisotropy parameter. In addition, for small values of magnetic field the concurrence measure is appropriate indicator for quantum phase transition, but for large values of magnetic field the Berry phase shows a sharp changes in the phase transition points. The results show that the Berry phase and concurrence form a complementary system from phase transition point of view.