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NEWS
We will hold the oneline workshop, Tensor Network States: Algorithms and Applications (TNSAA) 20212022, from Jan. 17 to Jan. 21, 2022. The series of workshop, TNSAA, has been organized for the purposes of exchanging new developments, having discussions toward future studies, and providing intruductory talks for new generation of researchers about tensor networks.
 Date
 May 31, 2021
 Seminar
 StatPhys seminar at University of Tokyo, Hongo, Japan
 Title
 Universal spectrum structure on the nonequilibrium critical line of the onedimensional DomanyKinzel cellular automaton
 Abstract

The DomanyKinzel(DK) cellular automaton is a stochastic timeevolutional system with an absorbing state from which the system cannot escape and a canonical model for nonequilibrium critical phenomena[1]. We introduce the tensor network method as a new tool to study it. Estimating the entropy of the DK automaton with a matrix product state representation of distribution, we reported a new cusp of the Renyi entropy in the active phase of the DK cellular automaton[2]. We recently applied a tensor renormalization group method to transfer matrices at the nonequilibrium critical point of the DK cellular automaton, confirming a universal spectrum structure[3]. In this talk, we will report our results with a brief review of models and methods.
[1] M. Henkel, H. Hinrichsen, and S. Lübeck, NonEquilibrium Phase Transitions. Volume 1: Absorbing Phase Transitions, Vol. 1 (Springer, 2008).
[2] K. H. and N. Kawashima, Entropy Governed by the Absorbing State of Directed Percolation, Physical Review Letters 123, 090601 (2019).
[3] K. H., Universal spectrum structure at nonequilibrium critical points in the (1+1)dimensional directed percolation, arXiv:2008.10807.
 Title
 Critical exponents in coupled phaseoscillator models on smallworld networks
 Reference
 Physical Review E 102, 062212 (2020)
 DOI
 10.1103/PhysRevE.102.062212
 Author
 Ryosuke Yoneda, Kenji Harada, and Yoshiyuki Y. Yamaguchi
 Abstract
 A coupled phaseoscillator model consists of phase oscillators, each of which has the natural frequency obeying a probability distribution and couples with other oscillators through a given periodic coupling function. This type of model is widely studied since it describes the synchronization transition, which emerges between the nonsynchronized state and partially synchronized states. The synchronization transition is characterized by several critical exponents, and we focus on the critical exponent defined by coupling strength dependence of the order parameter for revealing universality classes. In a typical interaction represented by the perfect graph, an infinite number of universality classes is yielded by dependency on the natural frequency distribution and the coupling function. Since the synchronization transition is also observed in a model on a smallworld network, whose number of links is proportional to the number of oscillators, a natural question is whether the infinite number of universality classes remains in smallworld networks irrespective of the order of links. Our numerical results suggest that the number of universality classes is reduced to one and the critical exponent is shared in the considered models having coupling functions up to second harmonics with unimodal and symmetric natural frequency distributions.
 Comments
 8 pages, 8 figures
 Preprint
 arXiv:2007.04539
 Preprint
 arXiv:2008.10807
 Author
 Kenji Harada
 Abstract
 Using a tensor renormalization group method with oblique projectors for an anisotropic tensor network, we confirm that the rescaled spectrum of transfer matrices at nonequilibrium critical points in the (1+1)dimensional directed percolation, a canonical model of nonequilibrium critical phenomena, is scaleinvariant and its structure is universal.
 Comments
 6 pages, 7 figures
 Title
 Finitem scaling analysis of BerezinskiiKosterlitzThouless phase transitions and entanglement spectrum for the sixstate clock model
 Reference
 Physical Review E 101, 062111 (2020)
 DOI
 10.1103/PhysRevE.101.062111
 Author
 Hiroshi Ueda, Kouichi Okunishi, Kenji Harada, Roman Krčmár, Andrej Gendiar, Seiji Yunoki, and Tomotoshi Nishino
 Abstract
 We investigate the BerezinskiiKosterlitzThouless transitions for the squarelattice sixstate clock model with the cornertransfer matrix renormalization group (CTMRG). Scaling analyzes for effective correlation length, magnetization, and entanglement entropy with respect to the cutoff dimension m at the fixed point of CTMRG provide transition temperatures consistent with a variety of recent numerical studies. We also reveal that the fixed point spectrum of the corner transfer matrix in the critical intermediate phase of the sixstate clock model is characterized by the scaling dimension consistent with the c=1 boundary conformal field theory associated with the effective Z_6 dual sineGordon model.
 Comments
 7 pages, 7 figures
 Preprint
 arXiv:2001.10176
 Conference: Tensor Network States: Algorithms and Applications (TNSAA) 20192020
 Invited talk: "New numerical approaches for directed percolation"
 Date: Dec. 4, 2019
 Conference dates: Dec. 46, 2019
 Venue: NCCU, Taipei, TAIWAN
 URL：https://tnsaa7.github.io
TOPICS
Toolkit of Bayesian Scaling Analysis
Reference application software of a new scaling analysis method of critical phenomena based on Bayesian inference.
To demo To detailsMonte Carlo simulations
This demonstration shows a Monte Carlo simulation of the twodimensional Ising model by three algorithms: Metropolis, SwendsenWang, and Wolff algorithms.
To demoABOUT
Kenji Harada
(
原田健自
)
Assistant Professor,
Graduate School of Informatics, Kyoto University, Japan.
harada@acs.i.kyotou.ac.jp
Room 203, Research Bldg. No.8, Yoshida Campus, Kyoto Univ., Kyoto, 6068501, Japan.
Map (No.59)