Principal component analysis of diffuse magnetic neutron scattering: a theoretical study

Twyman, Robert; Gibson, Stuart J.; Molony, James; Quintanilla, Jorge

doi:10.1088/1361-648x/ac056f

Cited by 3 publications

(3 citation statements)

References 38 publications

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“…We note that the work in Ref. [8] dealt with classical models however similar dimensionality-reduction has been shown for quantum models using closely-related Principal Component Analysis [20].…”

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confidence: 67%

“…Our last result offers the possibility to study systems for which experimental magnetic neutron scattering data is available by working directly with the wave function, without the need for a model Hamiltonian. Compared to the machine learning based approaches commented on above [8,20] the process here would be much swifter as rather than multiple optimisations carried out for different model Hamiltonians a single optimisation loop would be required. For instance, one could encode the wave function in a neural network, trained once to reproduce the experimental data.…”

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confidence: 99%

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Relationship between the wave function of a magnet and its static structure factor

Quintanilla

2022

Phys. Rev. B

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We state and prove two theorems about the ground state of magnetic systems described by very general Heisenberg-type models. The first theorem states that the relationship between the Hamiltonian and the ground-state correlators is invertible. The second theorem states that the relationship between the wave function and the correlators is also invertible. We discuss the implications of these theorems for neutron scattering. We propose, in particular, a variational approach to quantum magnets where a representation of the wave function (held, for instance, in a neural network or in the qubit register of a quantum processor) is optimised to fit experimental neutron-scattering data directly, without the involvement of a model Hamiltonian.

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confidence: 67%

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confidence: 99%

Relationship between the wave function of a magnet and its static structure factor

Quintanilla

2022

Phys. Rev. B

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“…Specifically in condensed matter physics, ML is well suited for many tasks ranging from predicting materials properties based on existing databases and pattern recognition in specific experimental data to analysing theoretical models of quantum materials. Prominent examples include the prediction of novel materials [4,5,6], identification of phase transitions in models of magnetic materials starting from Ising models [7,8,9,10,11,12], reaching complex spin liquids in Heisenberg systems [13] and the detection of entanglement transitions from simulated neutron scattering data [14]. Machine learning algorithms were also proven to be state of the art techniques in simulations of wave functions [15] or density matrices [16,17,18,19] for many-body quantum systems and the tomographic reconstruction of many-body wave functions from experimental data [20].…”

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confidence: 99%

Machine Learning approach to muon spectroscopy analysis

Tula,

Möller,

Quintanilla

et al. 2020

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In recent years, Artificial Intelligence techniques have proved to be very successful when applied to problems in physical sciences.Here we apply an unsupervised Machine Learning (ML) algorithm called Principal Component Analysis (PCA) as a tool to analyse the data from muon spectroscopy experiments. Specifically, we apply the ML technique to detect phase transitions in various materials. The measured quantity in muon spectroscopy is an asymmetry function, which may hold information about the distribution of the intrinsic magnetic field in combination with the dynamics of the sample. Sharp changes of shape of asymmetry functions -measured at different temperatures -might indicate a phase transition. Existing methods of processing the muon spectroscopy data are based on regression analysis, but choosing the right fitting function requires knowledge about the underlying physics of the probed material. Conversely, Principal Component Analysis focuses on small differences in the asymmetry curves and works without any prior assumptions about the studied samples. We discovered that the PCA method works well in detecting phase transitions in muon spectroscopy experiments and can serve as an alternative to current analysis, especially if the physics of the studied material are not entirely known. Additionally, we found out that our ML technique seems to work best with large numbers of measurements, regardless of whether the algorithm takes data only for a single material or whether the analysis is performed simultaneously for many materials with different physical properties.

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Relationship between the ground-state wave function of a magnet and its static structure factor

Quintanilla¹

2022

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Principal component analysis of diffuse magnetic neutron scattering: a theoretical study

Abstract: The version in the Kent Academic Repository may differ from the final published version. Users are advised to check http://kar.kent.ac.uk for the status of the paper. Users should always cite the published version of record.

Cited by 3 publications

References 38 publications

Relationship between the wave function of a magnet and its static structure factor

Relationship between the wave function of a magnet and its static structure factor

Machine Learning approach to muon spectroscopy analysis

Relationship between the ground-state wave function of a magnet and its static structure factor

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