Impacts of Intrinsic Noise and Quantum Entanglement on the Geometric and Dynamical Properties of the XXZ Heisenberg Interacting Spin Model

TL;DR

This paper investigates how intrinsic noise and quantum entanglement influence the geometric and dynamical properties of an XXZ Heisenberg spin model, revealing that decoherence suppresses entanglement and affects quantum speeds and phases.

Contribution

It introduces a unified framework analyzing the effects of intrinsic decoherence on entanglement, quantum speeds, and geometric phases in the XXZ Heisenberg model, highlighting the Hilbert-Schmidt speed's sensitivity.

Findings

Intrinsic noise rapidly suppresses entanglement.

Hilbert-Schmidt speed is more responsive to entanglement loss.

Decoherence hinders geometric phase accumulation, entanglement enhances it.

Abstract

Understanding how intrinsic decoherence affects the interplay between geometry, dynamics, and entanglement in quantum systems is a central challenge in quantum information science. In this work, we develop a unified framework that explores this interplay for a pair of interacting spins governed by an XXZ-type Heisenberg model under an external magnetic field and intrinsic decoherence. We quantify entanglement using the concurrence measure and examine its evolution under decoherence, revealing that intrinsic noise rapidly suppresses entanglement as it increases. We then analyze the Hilbert-Schmidt and Bures distances between quantum states and show how both the degree of entanglement and the noise rate modulate these distances and their associated quantum speeds. Importantly, we demonstrate that the Hilbert Schmidt speed is more responsive to entanglement and coherence loss than the Bures speed, making it a powerful tool for probing the geometry of quantum dynamics. Moreover, we solve the quantum brachistochrone problem in the presence of intrinsic decoherence, identifying the minimal evolution time and the corresponding optimal entangled states. Finally, we explore the geometric phase accumulated during the system's evolution. Our results show that decoherence hinders geometric phase accumulation, while entanglement counteracts this effect, enhancing phase stability.