# Interpreting machine learning of topological quantum phase transitions

## Abstract

There has been growing excitement over the possibility of employing artificial neural networks (ANNs) to gain new theoretical insight into the physics of quantum many-body problems. “Interpretability” remains a concern: can we understand the basis for the ANN’s decision-making criteria in order to inform our theoretical understanding? “Interpretable” machine learning in quantum matter has to date been restricted to linear models, such as support vector machines, due to the greater difficulty of interpreting nonlinear ANNs. Here we consider topological quantum phase transitions in models of Chern insulator, Z_{2} topological insulator, and Z_{2} quantum spin liquid, each using a shallow fully connected feed-forward ANN. The use of quantum loop topography, a “domain knowledge”–guided approach to feature selection, facilitates the construction of faithful phase diagrams and semiquantitative interpretation of the criteria in certain cases. To identify the topological phases, the ANNs learn physically meaningful features, such as topological invariants and deconfinement of loops. The interpretability in these cases suggests hope for theoretical progress based on future uses of ANN-based machine learning on quantum many-body problems.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division

- OSTI Identifier:
- 1632033

- Alternate Identifier(s):
- OSTI ID: 1733302

- Grant/Contract Number:
- SC0018946

- Resource Type:
- Published Article

- Journal Name:
- Physical Review Research

- Additional Journal Information:
- Journal Name: Physical Review Research Journal Volume: 2 Journal Issue: 2; Journal ID: ISSN 2643-1564

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Machine learning; Topological insulators; Topological phases of matter; Artificial neural networks

### Citation Formats

```
Zhang, Yi, Ginsparg, Paul, and Kim, Eun-Ah. Interpreting machine learning of topological quantum phase transitions. United States: N. p., 2020.
Web. doi:10.1103/PhysRevResearch.2.023283.
```

```
Zhang, Yi, Ginsparg, Paul, & Kim, Eun-Ah. Interpreting machine learning of topological quantum phase transitions. United States. doi:https://doi.org/10.1103/PhysRevResearch.2.023283
```

```
Zhang, Yi, Ginsparg, Paul, and Kim, Eun-Ah. Thu .
"Interpreting machine learning of topological quantum phase transitions". United States. doi:https://doi.org/10.1103/PhysRevResearch.2.023283.
```

```
@article{osti_1632033,
```

title = {Interpreting machine learning of topological quantum phase transitions},

author = {Zhang, Yi and Ginsparg, Paul and Kim, Eun-Ah},

abstractNote = {There has been growing excitement over the possibility of employing artificial neural networks (ANNs) to gain new theoretical insight into the physics of quantum many-body problems. “Interpretability” remains a concern: can we understand the basis for the ANN’s decision-making criteria in order to inform our theoretical understanding? “Interpretable” machine learning in quantum matter has to date been restricted to linear models, such as support vector machines, due to the greater difficulty of interpreting nonlinear ANNs. Here we consider topological quantum phase transitions in models of Chern insulator, Z2 topological insulator, and Z2 quantum spin liquid, each using a shallow fully connected feed-forward ANN. The use of quantum loop topography, a “domain knowledge”–guided approach to feature selection, facilitates the construction of faithful phase diagrams and semiquantitative interpretation of the criteria in certain cases. To identify the topological phases, the ANNs learn physically meaningful features, such as topological invariants and deconfinement of loops. The interpretability in these cases suggests hope for theoretical progress based on future uses of ANN-based machine learning on quantum many-body problems.},

doi = {10.1103/PhysRevResearch.2.023283},

journal = {Physical Review Research},

number = 2,

volume = 2,

place = {United States},

year = {2020},

month = {6}

}

DOI: https://doi.org/10.1103/PhysRevResearch.2.023283

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