Learning disordered topological phases by statistical recovery of symmetry

Yoshioka, Nobuyuki; Akagi, Yutaka; Katsura, Hosho

doi:10.1103/physrevb.97.205110

Cited by 79 publications

(45 citation statements)

References 62 publications

(74 reference statements)

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“…Introduction -Artificial neural networks (ANN) for machine learning (ML) are quickly becoming an indispensable tool not just in every-day life applications like voice recognition, but also in fundamental sciences. In the context of applied statistical physics, for instance, machine learning techniques have been used successfully for classifying phases of matter and phase transitions [1][2][3][4][5][6], speeding up Monte Carlo simulations [7,8], molecular modelling [9,10] and more. These applications are close in spirit to classical ML tasks, in that the networks are trained using labelled data such that they learn to approximate a certain target function known on a finite number of data points.…”

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confidence: 99%

Symmetries and Many-Body Excitations with Neural-Network Quantum States

et al. 2018

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Artificial neural networks have been recently introduced as a general ansatz to compactly represent manybody wave functions. In conjunction with Variational Monte Carlo, this ansatz has been applied to find Hamiltonian ground states and their energies. Here we provide extensions of this method to study properties of excited states, a central task in several many-body quantum calculations. First, we give a prescription that allows to target eigenstates of a (nonlocal) symmetry of the Hamiltonian. Second, we give an algorithm that allows to compute low-lying excited states without symmetries. We demonstrate our approach with both Restricted Boltzmann machines states and feedforward neural networks as variational wave-functions. Results are shown for the one-dimensional spin-1/2 Heisenberg model, and for the one-dimensional Bose-Hubbard model. When comparing to available exact results, we obtain good agreement for a large range of excited-states energies. Interestingly, we also find that deep networks typically outperform shallow architectures for high-energy states. arXiv:1807.03325v1 [cond-mat.str-el] 9 Jul 2018

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confidence: 99%

Symmetries and Many-Body Excitations with Neural-Network Quantum States

et al. 2018

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“…Appendix). Testing various other approaches, such as the transfer matrix method [25,[40][41][42]52], will be an interesting future problem.…”

Section: Summary and Discussionmentioning

confidence: 99%

Phase diagram of a disordered higher-order topological insulator: A machine learning study

2019

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A higher-order topological insulator is a new concept of topological states of matter, which is characterized by the emergent boundary states whose dimensionality is lower by more than two compared with that of the bulk, and draws a considerable interest. Yet, its robustness against disorders is still unclear. In this work, we investigate a phase diagram of higher-order topological insulator phases in a breathing kagome model in the presence of disorders, by using a state-of-the-art machine learning technique. We find that the corner states survive against the finite strength of disorder potential as long as the energy gap is not closed, indicating the stability of the higher-order topological phases against the disorders. arXiv:1809.09865v2 [cond-mat.dis-nn]

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“…Topological phases form a central class of such phases. Though there has been recent progress in using machine learning for topological phases 3,4,9,12,15,19,30,31 , these early efforts naturally centered around benchmarking the neural network based approaches to the conventional approaches on established problems by suppressing either disorder or interaction.…”

Section: Introductionmentioning

confidence: 99%

Multifaceted machine learning of competing orders in disordered interacting systems

et al. 2019

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While the non-perturbative interaction effects in the fractional quantum Hall regime can be readily simulated through exact diagonalization, it has been challenging to establish a suitable diagnostic that can label different phases in the presence of competing interactions and disorder. Here we introduce a multi-faceted framework using a simple artificial neural network (ANN) to detect defining features of a fractional quantum Hall state, a charge density wave state and a localized state using the entanglement spectra and charge density as independent input. We consider the competing effects of a perturbing interaction (l = 1 pseudopotential ∆V1), a disorder potential W , and the Coulomb interaction to the system at filling fraction ν = 1/3. Our phase diagram benchmarks well against previous estimates of the phase boundary using conventional measures along the ∆V1 = 0 and W = 0 axes, the only regions where conventional approaches have been explored. Moreover, exploring the entire two-dimensional phase diagram for the first time, we establish the robustness of the fractional quantum Hall state and map out the charge density wave micro-emulsion phase wherein droplets of charge density wave region appear before the charge density wave is completely disordered. Hence we establish that the ANN can access and learn the defining traits of topological as well as broken symmetry phases using multi-faceted inputs of entanglement spectra and charge density.

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Learning disordered topological phases by statistical recovery of symmetry

Cited by 79 publications

References 62 publications

Symmetries and Many-Body Excitations with Neural-Network Quantum States

Symmetries and Many-Body Excitations with Neural-Network Quantum States

Phase diagram of a disordered higher-order topological insulator: A machine learning study

Multifaceted machine learning of competing orders in disordered interacting systems

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