# Identifying topological order through unsupervised machine learning

@article{RodriguezNieva2018IdentifyingTO, title={Identifying topological order through unsupervised machine learning}, author={J. Rodriguez-Nieva and M. S. Scheurer}, journal={Nature Physics}, year={2018}, pages={1-6} }

The Landau description of phase transitions relies on the identification of a local order parameter that indicates the onset of a symmetry-breaking phase. In contrast, topological phase transitions evade this paradigm and, as a result, are harder to identify. Recently, machine learning techniques have been shown to be capable of characterizing topological order in the presence of human supervision. Here, we propose an unsupervised approach based on diffusion maps that learns topological phase… Expand

#### 88 Citations

Unsupervised identification of topological phase transitions using predictive models

- Physics, Mathematics
- 2019

Machine-learning driven models have proven to be powerful tools for the identification of phases of matter. In particular, unsupervised methods hold the promise to help discover new phases of matter… Expand

Topological Quantum Phase Transitions Retrieved from Manifold Learning

- Physics
- 2020

The discovery of topological features of quantum states plays a central role in modern condensed matter physics and various artificial systems. Due to the absence of local order parameters, the… Expand

Unsupervised learning of topological phase diagram using topological data analysis

- Physics
- 2021

Topology and machine learning are two actively researched topics not only in condensed matter physics, but also in data science. Here, we propose the use of topological data analysis in unsupervised… Expand

Machine learning topological phases in real space

- Physics, Computer Science
- ArXiv
- 2019

The discovery of Shannon information entropy signals associated with topological phase transitions from the analysis of data from several thousand SSH systems illustrates how model explainability in machine learning can advance the research of exotic quantum materials with properties that may power future technological applications such as qubit engineering for quantum computing. Expand

Unsupervised identification of Floquet topological phase boundaries

- Physics
- 2021

Nonequilibrium topological matter has been a fruitful topic of both theoretical and experimental interest. A great variety of exotic topological phases unavailable in static systems may emerge under… Expand

Identifying Topological Phase Transitions in Experiments Using Manifold Learning.

- Physics, Medicine
- Physical review letters
- 2020

The ability of this approach to identify topological phase transitions even when the data originates from a small part of the system, and does not even include edge states, is demonstrated. Expand

Investigation of hidden multipolar spin order in frustrated magnets using interpretable machine learning techniques

- Physics
- 2019

Frustration gives rise to a plethora of intricate phenomena, the most salient of which are spin liquids, both classical ones—such as the spin-ice phase which has been realized experimentally in… Expand

Unsupervised learning eigenstate phases of matter

- Computer Science, Physics
- 2019

This work uses readily available clustering algorithms to extract the distinct eigenstate phases of matter within the transverse-field Ising model in the presence of interactions and disorder to produce phase diagrams and identify phase boundaries when local order parameters are unavailable. Expand

Unsupervised machine learning of phase transition in percolation

- Computer Science
- 2020

It is shown that one may identify phase transition in percolation from raw data under unsupervised machine learning by using the principal component analysis with the preprocessing treatment of the unpercolating clusters. Expand

Machine learning spectral indicators of topology

- Computer Science, Physics
- 2020

It is shown that XAS can potentially uncover materials' topology when augmented by machine learning, and the proposed machine learning-empowered XAS topological indicator has the potential to discover broader categories of topological materials, such as non-cleavable compounds and amorphous materials. Expand

#### References

SHOWING 1-10 OF 86 REFERENCES

Learning phase transitions by confusion

- Physics
- 2017

A neural-network technique can exploit the power of machine learning to mine the exponentially large data sets characterizing the state space of condensed-matter systems. Topological transitions and… Expand

Machine learning of phase transitions in the percolation and XY models.

- Physics, Medicine
- Physical review. E
- 2019

It is found that using just one hidden layer in a fully connected neural network, the percolation transition can be learned and the data collapse by using the average output layer gives correct estimate of the critical exponent ν. Expand

Machine learning vortices at the Kosterlitz-Thouless transition

- Physics, Mathematics
- 2018

Efficient and automated classification of phases from minimally processed data is one goal of machine learning in condensed matter and statistical physics. Supervised algorithms trained on raw… Expand

Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination.

- Computer Science, Physics
- Physical review. E
- 2017

It is demonstrated that quantified principal components from PCA not only allow the exploration of different phases and symmetry-breaking, but they can distinguish phase-transition types and locate critical points in frustrated models such as the triangular antiferromagnet. Expand

Quantum phase recognition via unsupervised machine learning

- Physics
- 2017

The application of state-of-the-art machine learning techniques to statistical physic problems has seen a surge of interest for their ability to discriminate phases of matter by extracting essential… Expand

Learning disordered topological phases by statistical recovery of symmetry

- Mathematics, Physics
- 2017

This letter applies the artificial neural network in a supervised manner to map out the quantum phase diagram of disordered topological superconductor in class DIII, and shows that the result is totally consistent with the calculation by the transfer matrix method or noncommutative geometry approach. Expand

Machine learning Z 2 quantum spin liquids with quasiparticle statistics

- Mathematics, Physics
- 2017

After decades of progress and effort, obtaining a phase diagram for a strongly correlated topological system still remains a challenge. Although in principle one could turn to Wilson loops and… Expand

Machine learning of frustrated classical spin models (II): Kernel principal component analysis

- Physics
- 2018

In this work, we apply a principal component analysis (PCA) method with a kernel trick to study the classification of phases and phase transitions in classical XY models of frustrated lattices.… Expand

Machine learning phases of matter

- Physics, Computer Science
- 2016

It is shown that modern machine learning architectures, such as fully connected and convolutional neural networks, can identify phases and phase transitions in a variety of condensed-matter Hamiltonians. Expand

Machine learning of frustrated classical spin models. I. Principal component analysis

- Computer Science, Physics
- 2017

This work feeds the compute with data generated by the classical Monte Carlo simulation for the XY model in frustrated triangular and union jack lattices, which has two order parameters and exhibits two phase transitions and shows that the outputs of the principle component analysis agree very well with the understanding of different orders in different phases. Expand