Multifaceted machine learning of competing orders in disordered interacting systems

Matty, Michael; Zhang, Yi; Papić, Zlatko; Kim, Eun-Ah

doi:10.1103/physrevb.100.155141

Title: Multifaceted machine learning of competing orders in disordered interacting systems

Journal Article · Mon Oct 28 00:00:00 EDT 2019 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.100.155141· OSTI ID:1802083

^[1]; Zhang, Yi ^[1]; Papić, Zlatko ^[2]; Kim, Eun-Ah ^[1]

Cornell Univ., Ithaca, NY (United States)
Univ. of Leeds, Leeds (United Kingdom)

While the nonperturbative 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 multifaceted 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 ΔV₁) , a disorder potential W, and the Coulomb interaction to the system at filling fraction ν = 1/3. In this work, our phase diagram benchmarks well against previous estimates of the phase boundary along the axes of our phase diagram where other measures exist. Moreover, exploring the entire two-dimensional phase diagram, we establish the robustness of the fractional quantum Hall state and map out the charge-density-wave microemulsion phase wherein droplets of the 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 multifaceted inputs of entanglement spectra and charge density.

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Research Organization:: Cornell Univ., Ithaca, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC); W.M. Keck Foundation; Engineering and Physical Sciences Research Council (EPSRC); National Science Foundation (NSF)

Grant/Contract Number:: SC0010313; SC0018946; 392182; EP/R020612/1; NSF PHY-1748958

OSTI ID:: 1802083

Alternate ID(s):: OSTI ID: 2322508

Journal Information:: Physical Review. B, Vol. 100, Issue 15; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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