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Date
Jan 26, 2024
Conference
2024 Annual Meeting of the Physical Society of Taiwan, Topical Symposia:Many-body systems and advanced numerical methods
Title
Optimizing tensor network structure

Date
Jan 22, 2024
Conference
Mini-workshop: Tensor Network algorithms and applications 2024 (Taipei, Taiwan)
Title
Optimizing tensor network structure

Date
Aug 22, 2023
Conference
Tensor Network States: Algorithms and Applications 2023 (Shanghai, China)
Title
Tensor network study of one-dimensional stochastic processes

Date
Aug 8, 2023
Conference
The 28th International Conference on Statistical Physics, Statphys28 (Tokyot, Japan)
Title
Renormalization of non-equilibrium critical points in one-dimensional stochastic processes by tensor networks
Abstract
Non-equilibrium critical points often hold scaling invariance in the spatial and temporal directions. As seen in equilibrium cases, we know various universality classes of non-equilibrium critical points in stochastic processes. However, the direct renormalization of statistical processes is technically difficult. Recently, renormalization using tensor network representation was proposed and extended[1-4], and it is quite successful in equilibrium critical points. We extend the approach to stochastic processes using oblique projectors in the tensor renormalization group with higher-order singular value decomposition[5]. We report the universal property of time-evolution operators of one-dimensional contact processes of which critical points belong to the (1+1)-dimensional directed percolation(DP) universality class. The renormalized time-evolution operator has a universal spectrum structure of the (1+1)-dimensional DP universality class in spatial and temporal directions.
[1] M. Levin and C. P. Nave, Tensor Renormalization Group Approach to Two-Dimensional Classical Lattice Models, Physical Review Letters 99, 120601 (2007).
[2] Z. Y. Xie, J. Chen, M. P. Qin, J. W. Zhu, Y. P. L., and T. Xiang, Coarse-Graining Renormalization by Higher-Order Singular Value Decomposition, Physical Review B 86, 045139 (2012).
[3] G. Evenbly and G. Vidal, Tensor Network Renormalization, Physical Review Letters 115, 180405 (2015).
[4] K. Harada, Entanglement Branching Operator, Physical Review B 97, 045124 (2018).
[5] K. Harada, Universal spectrum structure at nonequilibrium critical points in the (1+1)-dimensional directed percolation, arXiv:2008.10807.

Title
Neural network approach to scaling analysis of critical phenomena
Reference
Physical Review E 107, 044128 (2023)
DOI
10.1103/PhysRevE.107.044128
Author
Ryosuke Yoneda and Kenji Harada
Abstract
Determining the universality class of a system exhibiting critical phenomena is one of the central problems in physics. There are several methods to determine this universality class from data. As methods to collapse plots onto scaling functions, polynomial regression, which is less accurate, and Gaussian process regression, which provides high accuracy and flexibility but is computationally expensive, have been proposed. In this paper, we propose a regression method using a neural network. The computational complexity is linear only in the number of data points. We demonstrate the proposed method for the finite-size scaling analysis of critical phenomena in the two-dimensional Ising model and bond percolation problem to confirm the performance. This method efficiently obtains the critical values with accuracy in both cases.
Comments
10 pages, 10 figures
Preprint
arXiv.2209.01777

Title
Quantum critical dynamics in the two-dimensional transverse Ising model
Reference
Physical Review Research 5, 013186 (2023)
DOI
10.1103/PhysRevResearch.5.013186
Author
Chisa Hotta, Tempei Yoshida, and Kenji Harada
Abstract
In the vicinity of the quantum critical point (QCP), thermodynamic properties diverge toward zero temperature governed by universal exponents. Although this fact is well known, how it is reflected in quantum dynamics has not been addressed. The QCP of the transverse Ising model on a triangular lattice is an ideal platform to test the issue, since it has an experimental realization, the dielectrics being realized in an organic dimer Mott insulator, κ−ET2X, where a quantum electric dipole represents the Ising degrees of freedom. We track the Glauber-type dynamics of the model by constructing a kinetic protocol based on the quantum Monte Carlo method. The dynamical susceptibility takes the form of the Debye function and shows a significant peak narrowing in approaching a QCP due to the divergence of the relaxation timescale. It explains the anomaly of dielectric constants observed in the organic materials, indicating that the material is very near the ferroelectric QCP. We disclose how the dynamical and other critical exponents develop near QCP beyond the simple field theory.
Comments
12 pages, 8 figures
Preprint
arXiv:2209.11599

TOPICS

Toolkit of Bayesian Scaling Analysis

Reference application software of a new scaling analysis method of critical phenomena based on Bayesian inference.

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Monte Carlo simulations

This demonstration shows a Monte Carlo simulation of the two-dimensional Ising model by three algorithms: Metropolis, Swendsen-Wang, and Wolff algorithms.

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ABOUT

Kenji Harada

Kenji Harada ( 原田健自 )
Assistant Professor, Graduate School of Informatics, Kyoto University, Japan.
harada.kenji.8e@kyoto-u.ac.jp
Room 203, Research Bldg. No.8, Yoshida Campus, Kyoto Univ., Kyoto, 606-8501, Japan. Map (No.59)

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