More is different.
God is in the details.
- Hiroshi Ueda, Kouichi Okunishi, Kenji Harada, Roman Krčmár, Andrej Gendiar, Seiji Yunoki, and Tomotoshi Nishino
- We investigate the Berezinskii-Kosterlitz-Thouless transitions for the square-lattice six-state clock model with the corner-transfer 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 six-state clock model is characterized by the scaling dimension consistent with the c=1 boundary conformal field theory associated with the effective Z_6 dual sine-Gordon model.
- 7 pages, 7 figures
- Conference: Tensor Network States: Algorithms and Applications (TNSAA) 2019-2020
- Invited talk: "New numerical approaches for directed percolation"
- Date: Dec. 4, 2019
- Conference dates: Dec. 4-6, 2019
- Venue: NCCU, Taipei, TAIWAN
- Entropy Governed by the Absorbing State of Directed Percolation
- Physical Review Letters 123, 090601 (2019)
- Kenji Harada and Naoki Kawashima
- We investigate the informational aspect of (1+1)-dimensional directed percolation, a canonical model of a nonequilibrium continuous transition to a phase dominated by a single special state called the “absorbing” state. Using a tensor network scheme, we numerically calculate the time evolution of state probability distribution of directed percolation. We find a universal relaxation of Rényi entropy at the absorbing phase transition point as well as a new singularity in the active phase, slightly but distinctly away from the absorbing transition point. At the new singular point, the second-order Rényi entropy has a clear cusp. There we also detect a singular behavior of “entanglement entropy,” defined by regarding the probability distribution as a wave function. The entanglement entropy vanishes below the singular point and stays finite above. We confirm that the absorbing state, though its occurrence is exponentially rare in the active phase, is responsible for these phenomena. This interpretation provides us with a unified understanding of time evolution of the Rényi entropy at the critical point as well as in the active phase.
- Title: Tensor network technique for stochastic process
- Date: July 17, 2019
- Title: Informational aspect of directed percolation problem
- Date: July 22, 2019
- Venue: The Institute for Solid State Physics, The University of Tokyo, JAPAN
- URL: http://www.issp.u-tokyo.ac.jp/public/caqmp2019/
- Kenji Harada and Naoki Kawashima
- We investigate the informational aspect of (1+1)-dimensional directed percolation(DP), a canonical model of a non-equilibrium continuous transition to a phase dominated by a single special state called the "absorbing" state. Using a tensor network scheme, we numerically calculate the time evolution of state probability distribution of DP. We find a universal relaxation of Renyi entropy at the absorbing phase transition point and a new singularity in the active phase where the second-order Renyi entropy has a cusp and the dynamical behavior of entanglement entropy changes from asymptotically-complete disentanglement to finite entanglement. We confirm that the absorbing state, though its occurrence is exponentially rare in the active phase, is responsible for these phenomena. This interpretation provides us with a unified understanding of time-evolution of the Renyi entropy at the critical point as well as in the active phase.
- 6(=4+1.5) pages, 8(=5+3) figures
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.To demo
Assistant Professor, Graduate School of Informatics, Kyoto University, Japan.
Room 203, Research Bldg. No.8, Yoshida Campus, Kyoto Univ., Kyoto, 606-8501, Japan. Map (No.59)