Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions

Ohtsuki, Tomi; Mano, Tomohiro

doi:10.7566/jpsj.89.022001

Cited by 53 publications

(41 citation statements)

References 375 publications

(356 reference statements)

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“…This procedure resembles research in the field of physics, in which physical principles are often deduced from accumulated experimental data. Therefore, machine learning techniques might have good compatibility with scientific research and have thus been applied to a wide variety of physical issues [3][4][5][6]. An ultimate goal of this research direction is to discover new physics through machine learning, but state-of-the-art machine-learning-based research in physics has not yet reached this stage.…”

Section: Introductionmentioning

confidence: 99%

Machine-learning detection of the Berezinskii-Kosterlitz-Thouless transitions in the q-state clock models

Miyajima,

Murata,

Tanaka

et al. 2021

Preprint

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We demonstrate that a machine learning technique with a simple feedforward neural network can sensitively detect two successive phase transitions associated with the Berezinskii-Kosterlitz-Thouless (BKT) phase in q-state clock models simultaneously by analyzing the weight matrix components connecting the hidden and output layers. We find that the method requires only a data set of the raw spatial spin configurations for the learning procedure. This data set is generated by Monte-Carlo thermalizations at selected temperatures. Neither prior knowledge of, for example, the transition temperatures, number of phases, and order parameters nor processed data sets of, for example, the vortex configurations, histograms of spin orientations, and correlation functions produced from the original spin-configuration data are needed, in contrast with most of previously proposed machine learning methods based on supervised learning. Our neural network evaluates the transition temperatures as T2/J = 0.921 and T1/J = 0.410 for the paramagnetic-to-BKT transition and BKT-to-ferromagnetic transition in the eight-state clock model on a square lattice. Both critical temperatures agree well with those evaluated in the previous numerical studies.

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Section: Introductionmentioning

confidence: 99%

Machine-learning detection of the Berezinskii-Kosterlitz-Thouless transitions in the q-state clock models

Miyajima,

Murata,

Tanaka

et al. 2021

Preprint

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show abstract

“…Due to its data-driven nature, a well-trained NNW model can learn to represent or encode each data point in a given large data set in terms of a more compact vector in internal (hidden) dimensions. DL thus can be efficiently applied for several types of tasks, such as approximating quantum wave functions [14][15][16][17][18][19][20][21][22][23] , assisting quantum simulations [24][25][26][27][28][29] , and detecting phases of matter [30][31][32][33][34][35][36][37][38][39][40][41] . In particular, DL has be shown not only to help recognize conventional, symmetry-breaking phase transitions but also to discover non-local, topological ones [42][43][44][45][46][47][48][49][50] .…”

Section: Introductionmentioning

confidence: 99%

Deep learning of topological phase transitions from entanglement aspects for two-dimensional chiral p-wave superconductors

Chung,

Cheng,

Huang

et al. 2021

Preprint

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Applying deep learning to investigate topological phase transitions (TPTs) becomes a useful method due to not only its ability to recognize patterns but also its statistical excellency to examine the mount of information carried by different types of data inputs. Among possible data types, entanglement-related quantities, such as Majorana correlation matrices (MCMs), one-particle entanglement spectra (OPES), and entanglement eigenvectors (OPEEs), have been proved effective, however, are to date mostly restricted to one dimension. Here, we propose practical input data forms based on those quantities to study TPTs and to compare the efficiency of each form on classic two-dimensional chiral p-wave superconductors via the deep learning approach. First, we find that different input forms, either matrices or tensors both originated from real MCMs, can affect the precise locations of the predicted transition points. Next, due to the complex nature of OPEEs, we extract three spatially dependent quantities from OPEEs, one related to the "intensity", and the other two related to "phases" of particle and hole components. We show that similar to taking OPES directly as inputs, solely using "intensity" quantity can only distinguish topological phases from trivial ones, whereas using either whole MCMs or complete OPEE-extracted quantities can provide sufficient information for deep learning to distinguish between phases of matter with different U (1) gauges or Chern numbers. Finally, we discuss certain characteristic features in the deep learning approach and, in particular, they reveal that our trained models indeed learn physically meaningful features, which confirms the potential use even at high dimensions.

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“…Examples include disordered systems, [32][33][34] topological phases, [35][36][37][38] and non-Hermitian systems 39,40) (see Ref. 41) for a review). These studies motivate us to employ CNN to the random flat-band models.…”

Section: Introductionmentioning

confidence: 99%

Machine Learning Study on the Flat-Band States Constructed by Molecular-Orbital Representation with Randomness

Kuroda,

Mizoguchi,

Araki

et al. 2021

Preprint

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We study the characteristic probability density distribution of random flat band models by machine learning. The models considered here are constructed on the basis of the molecular-orbital representation, which guarantees the existence of the macroscopically degenerate zero-energy modes even in the presence of randomness. We find that flat band states are successfully distinguished from conventional extended and localized states, indicating the characteristic feature of the flat band states. We also find that the flat band states can be detected when the target data are defined in the different lattice from the training data, which implies the universal feature of the flat band states constructed by the molecular-orbital representation.

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Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions

Cited by 53 publications

References 375 publications

Machine-learning detection of the Berezinskii-Kosterlitz-Thouless transitions in the q-state clock models

Machine-learning detection of the Berezinskii-Kosterlitz-Thouless transitions in the q-state clock models

Deep learning of topological phase transitions from entanglement aspects for two-dimensional chiral p-wave superconductors

Machine Learning Study on the Flat-Band States Constructed by Molecular-Orbital Representation with Randomness

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