Perturbational Decomposition Analysis for Quantum Ising Model with Weak Transverse Fields

• Published in: Entropy (Basel, Switzerland) Vol. 26; no. 12; p. 1094
• Main Authors: Li, Youning, Huang, Junfeng, Zhang, Chao, Li, Jun
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 14.12.2024; MDPI
• Subjects: Accuracy; Analysis; Artificial intelligence; Boundary conditions; Condensed matter physics; Decomposition; Decomposition method; Dimensional analysis; Ising model; Optimization; Parameters; Perturbation (Mathematics); perturbative approach; Phase transitions; Physics; quantum simulation; Simulation; Transverse waves; Weak interactions (Nuclear physics); China; perturbative approach; quantum simulation; Ising model
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e26121094

This work presents a perturbational decomposition method for simulating quantum evolution under the one-dimensional Ising model with both longitudinal and transverse fields. By treating the transverse field terms as perturbations in the expansion, our approach is particularly effective in systems with moderate longitudinal fields and weak to moderate transverse fields relative to the coupling strength. Through systematic numerical exploration, we characterize parameter regimes and evolution time windows where the decomposition achieves measurable improvements over conventional Trotter decomposition methods. The developed perturbational approach and its characterized parameter space may provide practical guidance for choosing appropriate simulation strategies in different parameter regimes of the one-dimensional Ising model.