Critical Dynamics of Transverse-field Quantum Ising Model using Finite-Size Scaling and Matrix Product States
The study of phase transition is usually done by numerical simulation of finite system. Conventional methods such as Monte Carlo simulations and phenomenological renormalization group methods obtain the critical exponents without obtaining the quantum wavefunction of the system. The Matrix Product States formalism allows one to obtain accurate numerical wavefunctions of short ranged interacting quantum many-body systems. In this study we combine the Finite Size Scaling theory and Matrix Product States formalism to study the critical dynamics of one-dimensional quantum Ising model. Finite size simulations of 20, 40, 60, 80, 100 and 120 spins are done using the Density Matrix Renormalization Group to obtain the ground state wavefunction of the system. The thermodynamic quantities such as the magnetization, susceptibility and correlation function are calculated. The critical exponents independently calculated are respectively β/ν = 0.1235(1), γ/ν = 1.7351(2), and η = 0.249(1). They conform with the theoretical values from analytical solution and fulfil the hyperscaling relation. We showed that both methods combined can reliably study the critical dynamics of one-dimensional Ising-like quantum lattice systems. Application of the study on water-ice phase transition of single-file water in nanopores is proposed.
KeywordsQuantum Ising model Finite-size Scaling Matrix Product States Binder’s Cumulant
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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