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

Abstract

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.

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Acknowledgements

The authors thank the Malaysian Ministry of Higher Education (MOHE) for FRGS grant: FP031-2017A and University of Malaya Frontier Research Grant: FG032-17AFR. S.Y. Pang thanks Dr. Miles Stoudenmire for his kind assistance in technical matters related to the ITensor Library. S.Y. Pang is supported by Skim Biasiswa MyBrainSc Scholarship under the Malaysian Ministry of Higher Education (MOHE).

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Correspondence to S. Y. Pang.

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Pang, S.Y., Muniandy, S.V. & Kamali, M.Z.M. Effect of Fluctuation in the Coupling Strength on Critical Dynamics of 1D Transverse Field Quantum Ising Model. Int J Theor Phys 59, 250–260 (2020) doi:10.1007/s10773-019-04320-3

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Keywords

  • Quantum Ising model
  • Random/Noisy Coupling
  • Matrix Product States
  • Critical Dynamics