Multifaceted machine learning of competing orders in disordered interacting systems

Abstract

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.

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

“…228,229) The interplay of randomness and interaction is attracting renewed interest from the view point of many-body localization, [230][231][232][233] where the hypothesis of "eigenstate thermalization" no longer applies, and the neural network is again shown to be powerful in recognizing whether the phase thermalizes. [234][235][236][237][238][239][240][241][242][243][244][245] In this paper, we review the application of the CNN to draw phase diagrams in random quantum systems. In the next section, we explain the methods, followed by a section on models and results, where the Anderson metal-insulator transitions and quantum percolation transitions in various dimensions, as well as the 3D topological insulator and Weyl semimetal transitions, are discussed.…”

Neural network setups for a precise detection of the many-body localization transition: Finite-size scaling and limitations

“…The recent application of machine learning techniques to condensed matter and statistical physics led to several and important successes in various problems, ranging from the detection of phases of matter from synthetic [1][2][3][4][5][6][7][8][9] or experimental data [10,11], wave-function reconstruction [12], the improvement of variational Ansätze for quantum problems [13][14][15][16][17][18], and efficient Monte Carlo sampling [19][20][21], in such a way that machine learning is now regarded as a new tool for the study of complex, interacting, (quantum) physical systems [22][23][24].…”

Conservation laws and spin system modeling through principal component analysis

“…The latter techniques are typified by cluster analysis, which classifies data into groups according to perceived similarities, and feature extraction, which projects the data set onto a low-dimensional space while still preserving essential characteristics of the original data. Examples of specific problems that have been examined with machine learning procedures are the simulation of quantum systems [18,[28][29][30][31][32], the prediction of crystal structures [33,34], the approximation of density functionals [35] and the solution of quantum impurity problems. [36] Additionally, machine learning can be employed to identify system properties and in particular can identify manifest and hidden order parameters and different phases or states of a system, especially when supplemented by additional knowledge of system properties such as locality, translational symmetry and symmetry breaking.…”