Perturbational Decomposition Analysis for Quantum Ising Model with Weak Transverse Fields

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Computational physics

Background:

• The one-dimensional Ising model is a fundamental model in statistical mechanics.
• Simulating quantum evolution accurately is crucial for understanding complex physical systems.
• Conventional Trotter decomposition methods have limitations in certain parameter regimes.

Purpose of the Study:

• To develop and present a novel perturbational decomposition method for simulating quantum evolution.
• To investigate the effectiveness of this method for the one-dimensional Ising model with longitudinal and transverse fields.
• To identify parameter regimes and evolution time windows where the new method outperforms conventional approaches.

Main Methods:

• A perturbational decomposition method is introduced, treating transverse field terms as perturbations.
• The method is applied to the one-dimensional Ising model with both longitudinal and transverse fields.
• Systematic numerical exploration is employed to characterize performance.

Main Results:

• The perturbational decomposition method shows measurable improvements over conventional Trotter decomposition.
• Effectiveness is particularly noted in systems with moderate longitudinal fields and weak to moderate transverse fields relative to coupling strength.
• Specific parameter regimes and evolution time windows for optimal performance are identified.

Conclusions:

• The developed perturbational approach offers a more effective simulation strategy for specific parameter regimes of the 1D Ising model.
• Characterized parameter spaces provide practical guidance for selecting simulation methods.
• This work contributes to advancing computational techniques in quantum many-body systems.