Engineering Topological Phases Guided by Statistical and Machine
Learning Methods
- URL: http://arxiv.org/abs/2008.11213v2
- Date: Wed, 17 Feb 2021 11:24:57 GMT
- Title: Engineering Topological Phases Guided by Statistical and Machine
Learning Methods
- Authors: Thomas Mertz and Roser Valent\'i
- Abstract summary: We propose a statistical method that is capable of constructing topological models for a generic lattice without prior knowledge of the phase diagram.
By sampling tight-binding parameter vectors from a random distribution we obtain data sets that we label with the corresponding topological index.
This labeled data is then analyzed to extract those parameters most relevant for the topological classification and to find their most likely values.
We present as a proof of concept the prediction of the Haldane model as the prototypical topological insulator for the honeycomb lattice in Altland-Zirnbauer (AZ) class A.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The search for materials with topological properties is an ongoing effort. In
this article we propose a systematic statistical method supported by machine
learning techniques that is capable of constructing topological models for a
generic lattice without prior knowledge of the phase diagram. By sampling
tight-binding parameter vectors from a random distribution we obtain data sets
that we label with the corresponding topological index. This labeled data is
then analyzed to extract those parameters most relevant for the topological
classification and to find their most likely values. We find that the marginal
distributions of the parameters already define a topological model. Additional
information is hidden in correlations between parameters. Here we present as a
proof of concept the prediction of the Haldane model as the prototypical
topological insulator for the honeycomb lattice in Altland-Zirnbauer (AZ) class
A. The algorithm is straightforwardly applicable to any other AZ class or
lattice and could be generalized to interacting systems.
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