ARCHIVES

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 scale-invariant and its structure is universal.
Comments
6 pages, 7 figures

2020-08-25-Paper-Universal-spectrum-DP.jpg

Preprint
arXiv:2007.04539
Title
Critical exponents in coupled phase-oscillator models on small-world networks
Author
Ryosuke Yoneda, Kenji Harada, Yoshiyuki Y. Yamaguchi
Abstract
A coupled phase-oscillator 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 models is widely studied since it describes the synchronization transition, which emerges between the non-synchronized state and partially synchronized states, and which is characterized by the critical exponents. Among them, we focus on the critical exponent defined by coupling strength dependence of the order parameter. The synchronization transition is not limited in the all-to-all interaction, whose number of links is of O(N2) with N oscillators, and occurs in small-world networks whose links are of O(N). In the all-to-all interaction, values of the critical exponent depend on the natural frequency distribution and the coupling function, classified into an infinite number of universality classes. A natural question is in small-world networks, whether the dependency remains irrespective of the order of links. To answer this question we numerically compute the critical exponent on small-world networks by using the finite-size scaling method with coupling functions up to the second harmonics and with unimodal and symmetric natural frequency distributions. Our numerical results suggest that, for the continuous transition, the considered models share the critical exponent 1/2, and that they are collapsed into one universality class.
Comments
7 pages, 7 figures

Title
Finite-m scaling analysis of Berezinskii-Kosterlitz-Thouless phase transitions and entanglement spectrum for the six-state 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 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.
Comments
7 pages, 7 figures
Preprint
arXiv:2001.10176

Preprint
arXiv:2001.10176
Author
Hiroshi Ueda, Kouichi Okunishi, Kenji Harada, Roman Krčmár, Andrej Gendiar, Seiji Yunoki, and Tomotoshi Nishino
Abstract
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.
Comments
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
  • URL:https://tnsaa7.github.io

TITLE
Entropy Governed by the Absorbing State of Directed Percolation
REFERENCE
Physical Review Letters 123, 090601 (2019)
DOI
10.1103/PhysRevLett.123.090601
AUTHOR
Kenji Harada and Naoki Kawashima
ABSTRACT
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.

2019-08-27-Paper-Renyi-DP.jpg

  • 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/

Preprint
arXiv:1902.10479
Author
Kenji Harada and Naoki Kawashima
Abstract
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.
Comments
6(=4+1.5) pages, 8(=5+3) figures

  • Title: "Entropy of the (1+1)-dimensional directed percolation"
  • Conference: International Conference on Advances in Physics of Emergent orders in Fluctuations (APEF2018)
  • Conference dates: November 12-15, 2018
  • Venue: The University of Tokyo, Tokyo, JAPAN
  • URL:https://apef2018.org

REFERENCE Physical Review B 97 (2018) 045124
DOI 10.1103/PhysRevB.97.045124
AUTHOR Kenji Harada
ABSTRACT We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a minimization problem based on squeezing operators. The entanglement branching is a new useful operation to manipulate a tensor network. For example, finding a particular entanglement structure by an entanglement branching operator, we can improve a higher-order tensor renormalization group method to catch a proper renormalization flow in a tensor network space. This new method yields a new type of tensor network states. The second example is a many-body decomposition of a tensor by using an entanglement branching operator. We can use it for a perfect disentangling among tensors. Applying a many-body decomposition recursively, we conceptually derive projected entangled pair states from quantum states that satisfy the area law of entanglement entropy.

Wei-Lin is a student in a doctoral course of National Taiwan University. His stay is financially supported by Japan-Taiwan Exchange Association.

International Symposium on Fluctuation and Structure out of Equilibrium 2017 (SFS2017)
  • Date of poster presentation: 14:50 ~ 16:50, 20th Nov. 2017.
  • Conference: International Symposium on Fluctuation and Structure out of Equilibrium 2017
  • Conference dates: From 20th Nov. 2017 to 23th Nov. 2017.
  • Venue: Sendai International Center, Sendai, Japan.
  • URL:http://sfs-dynamics.jp/sfs2017/

Title: "Entanglement branching operator" (invited)
  • Date of presentation: 14:00 ~ 15:00, 6th Nov. 2017.
  • Conference: Novel Quantum States in Condensed Matter 2017
  • Conference dates: From 23th Oct. 2017 to 24th Nov. 2017.
  • Venue: Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, Japan.
  • URL:http://www2.yukawa.kyoto-u.ac.jp/~nqs2017.ws/index.php
Preprint
arXiv:1710.01830
Abstract
We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a minimization problem based on squeezing operators. The entanglement branching is a new useful operation to manipulate a tensor network. For example, finding a particular entanglement structure by an entanglement branching operator, we can improve a higher-order tensor renormalization group method to catch a proper renormalization flow in a tensor network space. This new method yields a new type of tensor network states. The second example is a many-body decomposition of a tensor by using an entanglement branching operator. We can use it for a perfect disentangling among tensors. Applying a many-body decomposition recursively, we conceptually derive projected entangled pair states from quantum states that satisfy the area law of entanglement entropy.

Preprint
arXiv:1710.01830
Author
Kenji Harada
Abstract
We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a minimization problem based on squeezing operators. The entanglement branching is a new useful operation to manipulate a tensor network. For example, finding a particular entanglement structure by an entanglement branching operator, we can improve a higher-order tensor renormalization group method to catch a proper renormalization flow in a tensor network space. This new method yields a new type of tensor network states. The second example is a many-body decomposition of a tensor by using an entanglement branching operator. We can use it for a perfect disentangling among tensors. Applying a many-body decomposition recursively, we conceptually derive projected entangled pair states from quantum states that satisfy the area law of entanglement entropy.
Comments
9 pages, 11 figures

From 5 Feb. 2017 to 18 Feb. 2017, Workshop "Entanglement in Strongly Correlated Systems" , the Centro de Ciencias de Benasque Pedro Pascual, Benasque, Spain.

  • Title: "General Entanglement Branching in a Tensor Network" (invited)
  • Date of presentation: 14th Dec. 2016.
  • Conference: Fourth Workshop on Tensor Network States: Algorithms and Applications
  • Conference dates: From 12th Dec. 2016 to 15th Dec. 2016.
  • Venue: National Center for Theoretical Sciences, Hsinchu, Taiwan
  • URL:http://www.phys.cts.nthu.edu.tw/actnews/index.php?Sn=318

REFERENCE Physical Review B 92 (2015) 134404
DOI 10.1103/PhysRevB.92.134404
AUTHOR Tsuyoshi Okubo, Kenji Harada, Jie Lou, and Naoki Kaishima
ABSTRACT The SU(N) symmetric antiferromagnetic Heisenberg model with multicolumn representations on the two- dimensional square lattice is investigated by quantum Monte Carlo simulations. For the representation of a Young diagram with two columns, we confirm that a valence-bond solid (VBS) order appears as soon as the Néel order disappears at N = 10, indicating no intermediate phase. In the case of the representation with three columns, there is no evidence for either the Néel or the VBS ordering for N >= 15. This is actually consistent with the large-N theory, which predicts that the VBS state immediately follows the Néel state, because the expected spontaneous order is too weak to be detected.

REFERENCE Physical Review E 92 (2015) 012106
DOI 10.1103/PhysRevE.92.012106
AUTHOR Kenji Harada
ABSTRACT Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are corrections to scaling in many cases, and then the inference problem becomes ill-posed by an uncontrollable irrelevant scaling variable. We propose a new kernel method based on Gaussian process regression to fix this problem generally. We test the performance of the new kernel method for some example cases. In all cases, when the precision of the example data increases, inference results of the new kernel method correctly converge. Because there is no limitation in the new kernel method for the scaling function even with corrections to scaling, unlike in the conventional method, the new kernel method can be widely applied to real data in critical phenomena.
NOTE The reference code of this new method is prepared at http://kenjiharada.github.io/BSA/

BSA toolkit is a reference code of a new method for scaling analysis of critical phenomena. Using Bayesian inference, we automatically estimate critical point and indices. We fixed a bug for the output of scaling function with the option "-f 1". This bug does not affect the inference result of parameters.

PREPRINT arXiv:1504.05332
AUTHOR Tsuyoshi Okubo, Kenji Harada, Jie Lou, Naoki Kaishima
ABSTRACT The SU(N) symmetric antiferromagnetic Heisenberg model with multi-column representations on the two-dimensional square lattice is investigated by quantum Monte Carlo simulations. For the representation of Young diagram with two columns, we confirm that a valence-bond solid order appears as soon as the N'eel order disappears at N = 10 indicating no intermediate phase. In the case of the representation with three columns, there is no evidence for both of the N'eel and the valence-bond solid ordering for N >= 15. This is actually consistent with the large-N theory, which predicts that the VBS state immediately follows the N'eel state, because the expected spontaneous order is too weak to be detected.

REFERENCE Physical Review B 91 (2015) 094414
DOI 10.1103/PhysRevB.91.094414
AUTHOR Takafumi Suzuki, Kenji Harada, Haruhiko Matsuo, Synge Todo, and Naoki Kaishima
ABSTRACT We investigate thermal phase transitions to a valence-bond solid phase in SU(N) Heisenberg models with four- or six-body interactions on a square or honeycomb lattice, respectively. In both cases, a thermal phase transition occurs that is accompanied by rotational symmetry breaking of the lattice. We perform quantum Monte Carlo calculations in order to clarify the critical properties of the models. The estimated critical exponents indicate that the universality classes of the square- and honeycomb-lattice cases are identical to those of the classical XY model with a Z4 symmetry-breaking field and the three-state Potts model, respectively. In the square-lattice case, the thermal exponent, ν, monotonically increases as the system approaches the quantum critical point, while the values of the critical exponents, η and γ/ν, remain constant. From a finite-size scaling analysis, we find that the system exhibits weak universality, because the Z4 symmetry-breaking field is always marginal. In contrast, ν in the honeycomb-lattice case exhibits a constant value, even in the vicinity of the quantum critical point, because the Z3 field remains relevant in the SU(3) and SU(4) cases.

Title: ''Quantum Monte Carlo study of Quantum Criticality on SO(N) Bilinear Biquadratic Chains''
Date: Jan. 9, 2015
Conference: From Jan. 7, 2015 to Jan. 11, 2015, the 9th International Conference on Computational Physics (ICCP9) , National University of Singapore, Singapore.

Conference: 10sor network workshop --- Field 2x5 joint workshop on new algorithms for quantum manybody problems ---
Date: November 25, 2014, Tuedsay
Venue: Kashiwa Future Center, Kashiwa, Chiba, Japan
Title: "MERA tensor network and its application on quantum frustrated magnets"

From 20 Oct. 2014 to 22 Oct. 2014, the CMSI International Workshop 2014: Tensor Network Algorithms in Materials Science , RIKEN Advanced Institute for Computational Science 6F auditorium 7-1-26, Port Island South, Kobe, 650-0047, Japan.

The reference code of the new kernel method is added in the toolkit BSA. The new code can easily do the finite-size scaling analysis with or without corrections to scaling.

PREPRINT arXiv:1410.3622
AUTHOR Kenji Harada
ABSTRACT Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are corrections to scaling in many cases, and then the inference problem becomes ill-posed by an uncontrollable irrelevant scaling variable. We propose a new kernel method based on Gaussian process regression to fix this problem generally. We test the performance of the new kernel method for some example cases. In all cases, when the precision of the example data increases, inference results of the new kernel method correctly converge. Because there is no limitation in the new kernel method for the scaling function even with corrections to scaling, unlike in the conventional method, the new kernel method can be widely applied to real data in critical phenomena.

REFERENCE JPS Conf. Proc. 3 , 014031 (2014) [7 pages]
Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2013)
DOI 10.7566/JPSCP.3.014031
AUTHORKenji Harada
ABSTRACT We will introduce tensor network states in the variational calculation of ground states for quantum frustrated magnets. In particular, we will report the performance of MERA tensor network for an S = 1/2 antiferromagnetic Heisenberg model on a spatially anisotropic triangular lattice, which is an effective model of Mott insulators on a triangular layer of organic charge transfer salts.

REFERENCE Physical Review B 89 (2014) 134422
DOI 10.1103/PhysRevB.89.134422
PREPRINT arXiv:1312.2643
AUTHOR Kouichi Okunishi and Kenji Harada
ABSTRACT Using a generalized Jordan-Wigner transformation combined with the defining representation of the SO(N) spin, we map the SO(N) bilinear-biquadratic(BLBQ) spin chain into the N-color bosonic particle model. We find that, when the Jordan-Wigner transformation disentangles the symmetry-protected topological entanglement, this bosonic model becomes negative-sign free in the context of quantum Monte-Carlo simulation. For the SO(3) case, moreover, Kennedy-Tasaki's transformation for the S=1 BLBQ chain, which is also a topological disentangler, derives the same bosonic model through the dimer-R bases. We present temperature dependence of energy, entropy and string order parameter for the SO(N=3, 4, 5) BLBQ chains by the world-line Monte-Carlo simulation for the N-color bosonic particle model.

REFERENCE Physical Review Letters 112 (2014) 140603
DOI 10.1103/PhysRevLett.112.140603
PREPRINT arXiv:1307.0328
AUTHOR Akiko Masaki-Kato, Takafumi Suzuki, Kenji Harada, Synge Todo, Naoki Kaishima
ABSTRACT Based on the worm algorithm in the path-integral representation, we propose a general quantum Monte Carlo algorithm suitable for parallelizing on a distributed-memory computer by domain decomposition. Of particular importance is its application to large lattice systems of bosons and spins. A large number of worms are introduced and its population is controlled by a fictitious transverse field. For a benchmark, we study the size-dependence of the Bose-condensation order parameter of the hardcore Bose-Hubbard model with $L\times L\times \beta t = 10240\times 10240\times 16$, using 3200 computing cores, which shows good parallelization efficiency.

From 3 March 2014 to 7 March 2014,

  • Talk (Collaborator) "Parallelized Multi-Worm Algorithm for Large Scale Quantum Monte-Carlo simulations" C1.00284
  • Talk (Collaborator) "Thermal phase transitions to valence-bond-solid states in the two dimensional SU(N) Heisenberg models" F7.00010
  • Talk (Representative) "Possibility of Deconfined Criticality in SU(N) Heisenberg Models at Small N" S27.00013
APS March Meeting 2014, Denver, Colorado, USA.

Toolkit BSA is a reference code of a new method for scaling analysis of critical phenomena. Using Bayesian inference, we automatically estimate critical point and indices. This toolkit is announced in the MateriApps site.

REFERENCE Physical Review B 88 (2013) 220408(R)
DOI 10.1103/PhysRevB.88.220408
PREPRINT arXiv:1307.0501v2
AUTHOR Kenji Harada, Takafumi Suzuki, Tsuyoshi Okubo, Haruhiko Matsuo, Jie Lou, Hiroshi Watanabe, Synge Todo, and Naoki Kaishima
ABSTRACT To examine the validity of the scenario of the deconfined critical phenomena, we carry out a quantum Monte Carlo simulation for the SU($N$) generalization of the Heisenberg model with four-body and six-body interactions. The quantum phase transition between the SU($N$) N\'eel and valence-bond solid phases is characterized for $N=2,3,$ and $4$ on the square and honeycomb lattices. While finite-size scaling analysis works well up to the maximum lattice size ($L=256$) and indicates the continuous nature of the phase transition, a clear systematic change towards the first-order transition is observed in the estimates of the critical exponent $y \equiv 1/\nu$ as the system size increases. We also confirm the relevance of a squared valence-bond solid field $\Psi^2$ for the SU(3) model.

PREPRINT arXiv:1312.2643
AUTHOR Kouichi Okunishi and Kenji Harada
ABSTRACT Using a generalized Jordan-Wigner transformation combined with the defining representation of the SO(N) spin, we map the SO(N) bilinear-biquadratic(BLBQ) spin chain into the N-color bosonic particle model. We find that, when the Jordan-Wigner transformation disentangles the symmetry-protected topological entanglement, this bosonic model becomes negative-sign free in the context of quantum Monte-Carlo simulation. For the SO(3) case, moreover, Kennedy-Tasaki's transformation for the S=1 BLBQ chain, which is also a topological disentangler, derives the same bosonic model through the dimer-R bases. We present temperature dependence of energy, entropy and string order parameter for the SO(N=3, 4, 5) BLBQ chains by the world-line Monte-Carlo simulation for the N-color bosonic particle model.

From 21 Oct. 2013 to 22 Oct. 2013,
CMSI International Symposium 2013: "Extending the power of computational materials sciences with K-computer" , Ito International Research Center in the University of Tokyo, Hongo Campus in Tokyo, Japan.

From 28 July 2013 to 31 July 2013, "Statistical Physics of Quantum Matter", National Taiwan University, Taipei, Taiwan.

PREPRINT arXiv:1307.0328
AUTHOR Akiko Masaki-Kato, Takafumi Suzuki, Kenji Harada, Synge Todo, Naoki Kaishima
ABSTRACT Based on the worm algorithm in the path-integral representation, we propose a general quantum Monte Carlo algorithm suitable for parallelizing on a distributed-memory computer by domain decomposition. Of particular importance is its application to large lattice systems of bosons and spins. A large number of worms are introduced and its population is controlled by a fictitious transverse field. For a benchmark, we study the size-dependence of the Bose-condensation order parameter of the hardcore Bose-Hubbard model with $L \times L \times \beta t =10240 \times 10240 \times 16$, using 3200 computing cores, which shows good parallelization efficiency.

PREPRINT arXiv:1212.1999
AUTHOR Jie Lou, Takafumi Suzuki, Kenji Harada, and Naoki Kaishima
ABSTRACT We performed variational calculation based on the multi-scale entanglemnt renormalization ansatz, for the antiferromagnetic Heisenberg model on a Shastry Sutherland lattice (SSL). Our results show that at coupling ratio J'/J= 0.687(3), the system undergoes a quantum phase transition from the orthogonal dimer order to the plaquette valence bond solid phase, which then transits into the antiferromagnetic order above J'/J=0.75. In the presence of an external magnetic field, our calculations show clear evidences of various magnetic plateaux in systems with different coupling ratios range from 0.5 to 0.69. Our calculations are not limited to the small coupling ratio region, and we are able to show strong evidence of the presence of several supersolid phases, including ones above 1/2 and 1/3 plateaux. Such supersolid phases, which feature the coexistence of compressible superfluidity and crystalline long range order in triplet excitations, emerge at relatively large coupling ratio (J'/J>0.5). A schematic phase diagram of the SSL model in the presence of magnetic field is provided.

REFERENCE Physical Review B 86 (2012) 184421
DOI 10.1103/PhysRevB.86.184421
PREPRINT arXiv:1208.4306
AUTHOR Kenji Harada
ABSTRACT The ground state of an $S=1/2$ antiferromagnetic Heisenberg model on a spatially anisotropic triangular lattice, which is an effective model of Mott insulators on a triangular layer of organic charge transfer salts or Cs2CuCl4, is numerically studied. We apply a numerical variational method by using a tensor network with entanglement renormalization, which improves the capability of describing a quantum state. Magnetic ground states are identified for 0.7 <= J2 / J1 <= 1 in the thermodynamic limit, where J1 and J2 denote the innerchain and interchain coupling constants, respectively. Except for the isotropic case (J1 = J2), the magnetic structure is spiral with an incommensurate wave vector that is different from the classical one. The quantum fluctuation weakens the effective coupling between chains, but the magnetic order remains in the thermodynamic limit. In addition, the incommensurate wave number is in good agreement with that of the series expansion method.