Improving Understanding of Topological Phase Transitions

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Machine learning spots topological phase transitions in experimental data

Points to note…

+  A machine-learning tool called diffusion maps has been used to identify topological phase transitions in experimental data. The research was done by teams led by Mordechai Segev and Ronen Talmon at the Technion-Israel Institute of Technology[.] Their method requires no prior knowledge about the system, and it found a phase transition in the data that was not predicted by current theory. Their method can potentially help analyse data from complex quantum many-body experiments and improve our understanding of topological phases.

Topological phases are receiving increasing attention in condensed matter and optical systems because of their association with robust physical phenomena.

+  A recent addition to the familiar solid, liquid or gaseous phases of matter, topological phases have a non-local nature that makes them both interesting and challenging to detect. Technion’s Eran Lustig, one of the lead researchers on this work, uses the analogy of a tornado: one cannot tell that a tornado is a huge swirling vortex from just a tiny patch of it. Topological phases are typically identified by studying the unique evolution of edge states of the system, which requires access to a significant part of the material.

+  Or Yair, the other lead researcher on the project, explained that the diffusion-maps algorithm is well suited to detect non-local signatures of topological phases. Given a set of experimental data points, it checks the local neighbourhood of a point to find nearby points and gradually zooms out to find relationships with points that appear far apart.

+ Machine-learning tools also help researchers with the interpretation of the large amounts of data generated from modern experiments with many degrees of freedom. The diffusion-maps method is a kind of manifold learning algorithm, which tries to find a lower-dimensional representation of data. A simple example of dimensionality reduction is that of a line drawn on a 2D plane – while it appears that one needs two coordinates to specify points on a line, in reality it is just a 1D object or “manifold” embedded in a 2D space.

Source:  physicsworld.  Lavanya Taneja,  Machine learning spots topological phase transitions in experimental data…

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