Recent progress on cluster and meron algorithms for strongly correlated systems

Banerjee, Debasish

doi:10.1007/s12648-021-02155-5

Cited by 7 publications

(3 citation statements)

References 59 publications

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“…The current clustering algorithms are divided into five categories: density-based methods, grid-based methods, hierarchical-based methods, model-based methods, and division-based methods [3]. The Fuzzy C-means clustering method is a division-based clustering method, which is widely used in the segmentation and classification of brain tumors [4], the evaluation of power grid reliability performance [5], and the recognition of the whitewashing behavior of college accounting statements [6].…”

Section: Introductionmentioning

confidence: 99%

An Enhanced FCM Clustering Method Based on Multi-Strategy Tuna Swarm Optimization

Sun,

Shao,

Zhou

et al. 2024

Mathematics

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To overcome the shortcoming of the Fuzzy C-means algorithm (FCM)—that it is easy to fall into local optima due to the dependence of sub-spatial clustering on initialization—a Multi-Strategy Tuna Swarm Optimization-Fuzzy C-means (MSTSO-FCM) algorithm is proposed. Firstly, a chaotic local search strategy and an offset distribution estimation strategy algorithm are proposed to improve the performance, enhance the population diversity of the Tuna Swarm Optimization (TSO) algorithm, and avoid falling into local optima. Secondly, the search and development characteristics of the MSTSO algorithm are introduced into the fuzzy matrix of Fuzzy C-means (FCM), which overcomes the defects of poor global searchability and sensitive initialization. Not only has the searchability of the Multi-Strategy Tuna Swarm Optimization algorithm been employed, but the fuzzy mathematical ideas of FCM have been retained, to improve the clustering accuracy, stability, and accuracy of the FCM algorithm. Finally, two sets of artificial datasets and multiple sets of the University of California Irvine (UCI) datasets are used to do the testing, and four indicators are introduced for evaluation. The results show that the MSTSO-FCM algorithm has better convergence speed than the Tuna Swarm Optimization Fuzzy C-means (TSO-FCM) algorithm, and its accuracies in the heart, liver, and iris datasets are 89.46%, 63.58%, 98.67%, respectively, which is an outstanding improvement.

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Section: Introductionmentioning

confidence: 99%

An Enhanced FCM Clustering Method Based on Multi-Strategy Tuna Swarm Optimization

Sun,

Shao,

Zhou

et al. 2024

Mathematics

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“…Simultaneously, new classes of gauge theories, known as quantum link models, which realize continuous gauge invariance with finite dimensional Hilbert spaces [15], have widely extended the conventional reach of Wilson's lattice gauge theories [16]. Novel phases have been uncovered in such link models [17,18] using newly developed quantum Monte Carlo algorithms [19].…”

Section: Introductionmentioning

confidence: 99%

Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d

Hashizume¹,

Halimeh²,

Hauke³

et al. 2022

SciPost Phys.

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The exploration of phase diagrams of strongly interacting gauge theories coupled to matter in lower dimensions promises the identification of exotic phases and possible new universality classes, and it facilitates a better understanding of salient phenomena in Nature, such as confinement or high-temperature superconductivity. The emerging new techniques of quantum synthetic matter experiments as well as efficient classical computational methods with matrix product states have been extremely successful in one spatial dimension, and are now motivating such studies in two spatial dimensions. In this work, we consider a \mathrm{U}(1)U(1) quantum link lattice gauge theory where the gauge fields, represented by spin-\frac{1}{2}12 operators are coupled to a single flavor of staggered fermions. Using matrix product states on infinite cylinders with increasing diameter, we conjecture its phase diagram in (2+1)(2+1)-d. This model allows us to smoothly tune between the \mathrm{U}(1)U(1) quantum link and the quantum dimer models by adjusting the strength of the fermion mass term, enabling us to connect to the well-studied phases of those models. Our study reveals a rich phase diagram with exotic phases and interesting phase transitions to a potential liquid-like phase. It thus furthers the collection of gauge theory models that may guide future quantum-simulation experiments.

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“…Simultaneously, new classes of gauge theories, known as quantum link models, which realize continuous gauge invariance with finite dimensional Hilbert spaces 15 , have widely extended the conventional reach of Wilson's lattice gauge theories 16 . Novel phases have been uncovered in such link models 17,18 using newly developed quantum Monte Carlo algorithms 19 .…”

mentioning

confidence: 99%

Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d

Hashizume,

Halimeh,

Hauke

et al. 2021

Preprint

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Recent progress on cluster and meron algorithms for strongly correlated systems

Cited by 7 publications

References 59 publications

An Enhanced FCM Clustering Method Based on Multi-Strategy Tuna Swarm Optimization

An Enhanced FCM Clustering Method Based on Multi-Strategy Tuna Swarm Optimization

Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d

Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d

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