Effect of Fluctuation in the Coupling Strength on Critical Dynamics of 1D Transverse Field Quantum Ising Model

Pang, S.Y. and Muniandy, Sithi Vinayakam and Kamali, Mohd Zahurin Mohamed (2020) Effect of Fluctuation in the Coupling Strength on Critical Dynamics of 1D Transverse Field Quantum Ising Model. International Journal of Theoretical Physics, 59 (1). pp. 250-260. ISSN 0020-7748, DOI https://doi.org/10.1007/s10773-019-04320-3.

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Official URL: https://doi.org/10.1007/s10773-019-04320-3


The effect of uniformly distributed fluctuation in the coupling strength of a 100 spins transverse field quantum Ising chain is studied using the Density Matrix Renormalization Group on the Matrix Product States formalism. Uniform noise with mean zero and amplitude η is introduced to uniform nearest neighbour coupling of value unity. Disordered averages of thermodynamic quantities are calculated from 100 disordered realizations for each transverse field reading. We show that the system exhibits distinct behaviour of ordered and disordered state separated at η~1.0. For η ≲ 1.0, thermodynamic behaviour of the system gradually deviates from pure quantum Ising model. For η > 1.0 system exhibits highly fluctuating thermodynamic behaviour. Edward-Anderson order parameters are calculated and shown to be much less fluctuating and suitable as an order parameter for η > 1.0. Qualitative behaviour of the system is not affected by finite-size effect and replacing the fluctuation with normally distributed noise. Finally, for noise level between η = 1.0 and 1.5, the system exhibits a faster phase transition and enhances transverse magnetization before the critical point. For certain ranges of noise amplitude before the critical point, the quantum fluctuations are amplified. This suggests a potential improvement of quantum annealing within that regime. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Item Type: Article
Funders: Malaysian Ministry of Higher Education (MOHE) for FRGS grant: FP031-2017A, University of Malaya Frontier Research Grant: FG032-17AFR
Uncontrolled Keywords: Critical Dynamics; Matrix Product States; Quantum Ising model; Random/Noisy Coupling
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Centre for Foundation Studies in Science > Mathematics Division
Faculty of Science > Department of Physics
Depositing User: Ms. Juhaida Abd Rahim
Date Deposited: 19 Aug 2020 01:12
Last Modified: 19 Aug 2020 01:12
URI: http://eprints.um.edu.my/id/eprint/25416

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