Topologically invariant tensor renormalization group method for the Edwards-Anderson spin glasses model

Wang, Chuang; Qin, Shao-Meng; Zhou, Haijun

doi:10.1103/physrevb.90.174201

Cited by 22 publications

(11 citation statements)

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“…Exact contraction of a PEPS is #P hard [60]. Nevertheless, one can employ tensor renormalization group methods for approximated contraction of PEPS [61][62][63][64]. Thus, it remains to be seen whether judicious combination of these techniques really brings a better performance to generative modeling.…”

Section: Discussionmentioning

confidence: 99%

Unsupervised Generative Modeling Using Matrix Product States

et al. 2018

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Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum physics, we propose a generative model using matrix product states, which is a tensor network originally proposed for describing (particularly one-dimensional) entangled quantum states. Our model enjoys efficient learning analogous to the density matrix renormalization group method, which allows dynamically adjusting dimensions of the tensors and offers an efficient direct sampling approach for generative tasks. We apply our method to generative modeling of several standard data sets including the Bars and Stripes random binary patterns and the MNIST handwritten digits to illustrate the abilities, features, and drawbacks of our model over popular generative models such as the Hopfield model, Boltzmann machines, and generative adversarial networks. Our work sheds light on many interesting directions of future exploration in the development of quantum-inspired algorithms for unsupervised machine learning, which are promisingly possible to realize on quantum devices.

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Section: Discussionmentioning

confidence: 99%

Unsupervised Generative Modeling Using Matrix Product States

et al. 2018

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“…Recently, spin glasses (SG) have attracted much attention and stimulated intensive studies because the combination of quenched spin spatial randomness and frustration create a complex free energy landscape with multiple local energy minima and finding the stable spin states formidable challenging 1 2 3 . In spite of many theoretical attempts of developing renormalization group 1 4 , mean-field approximation 5 and Monte Carlo simulation 3 6 7 8 based analyses, the low-temperature ( T ) spin phases as well as the out-of-equilibrium aging dynamics of such materials remain matters of strong debates. Not surprisingly, the complex nature of SG spin structures gives rise to the unique and diverse macroscopic properties in many fields of science.…”

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confidence: 99%

Cooling field and temperature dependent exchange bias in spin glass/ferromagnet bilayers

Rui

et al. 2015

Sci Rep

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We report on the experimental and theoretical studies of cooling field (HFC) and temperature (T) dependent exchange bias (EB) in FexAu1 − x/Fe19Ni81 spin glass (SG)/ferromagnet (FM) bilayers. When x varies from 8% to 14% in the FexAu1 − x SG alloys, with increasing T, a sign-changeable exchange bias field (HE) together with a unimodal distribution of coercivity (HC) are observed. Significantly, increasing in the magnitude of HFC reduces (increases) the value of HE in the negative (positive) region, resulting in the entire HE ∼ T curve to move leftwards and upwards. In the meanwhile, HFC variation has weak effects on HC. By Monte Carlo simulation using a SG/FM vector model, we are able to reproduce such HE dependences on T and HFC for the SG/FM system. Thus this work reveals that the SG/FM bilayer system containing intimately coupled interface, instead of a single SG layer, is responsible for the novel EB properties.

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“…By repeating the same procedure, we can calculate the states of t ≥ 1, |P (t) . During the calculation of the time evolution, we truncate bond indices by singular-value decompositions if the bond dimensionality exceeds D. We can do these singular-value decompositions in the time of O(D 5 ) with a little ingenuity [29].…”

Section: A Transition Operator As Tensor-network Operatormentioning

confidence: 99%

Tensor-network algorithm for nonequilibrium relaxation in the thermodynamic limit

Hotta

2016

Phys. Rev. E

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We propose a tensor-network algorithm for discrete-time stochastic dynamics of a homogeneous system in the thermodynamic limit. We map a d-dimensional nonequilibrium Markov process to a (d+1)-dimensional infinite tensor network by using a higher-order singular-value decomposition. As an application of the algorithm, we compute the nonequilibrium relaxation from a fully magnetized state to equilibrium of the one- and two-dimensional Ising models with periodic boundary conditions. Utilizing the translational invariance of the systems, we analyze the behavior in the thermodynamic limit directly. We estimated the dynamical critical exponent z=2.16(5) for the two-dimensional Ising model. Our approach fits well with the framework of the nonequilibrium-relaxation method. Our algorithm can compute time evolution of the magnetization of a large system precisely for a relatively short period. In the nonequilibrium-relaxation method, one needs to simulate dynamics of a large system for a short time. The combination of the two provides a different approach to the study of critical phenomena.

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Topologically invariant tensor renormalization group method for the Edwards-Anderson spin glasses model

Cited by 22 publications

References 50 publications

Unsupervised Generative Modeling Using Matrix Product States

Unsupervised Generative Modeling Using Matrix Product States

Cooling field and temperature dependent exchange bias in spin glass/ferromagnet bilayers

Tensor-network algorithm for nonequilibrium relaxation in the thermodynamic limit

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