#### IMSc Webinar

#### Low Energy Theories of Quantum Magnets: Emergent Descriptions and Order by Singularity

#### Subhankar Khatua

##### IMSc

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Google Meet Link: meet.google.com/pnn-ccrt-yyv

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We present a paradigm to understand emergent behaviour in quantum magnets. At low energies, a magnet behaves as if it were a quantum particle moving on an abstract space. This space consists of classical minimum-energy configurations of the magnet.

If the minimum-energy configurations are all related to each other by symmetries, the emergent picture corresponds to a free particle problem. The particle explores every part of the space in a uniform fashion. However, if the space is larger than that allowed by symmetries, the particle samples the space unevenly. Each neighbourhood may be sampled with a different probability. In extreme cases, the probability is sharply peaked at a certain point and vanishes elsewhere — the particle localizes. This is a manifestation of the phenomenon of state selection in frustrated magnets.

We propose two distinct mechanisms by which localization of the emergent particle takes place; a) order by potential: the particle experiences a potential while moving on the space. If the potential has a sufficiently deep minimum, the particle localizes therein. b) Order by singularity: If the space is self-intersecting in nature, the particle may localize at the self-intersection point (singularity) without any localizing potential --- a consequence of the geometry of the space. We illustrate these ideas by taking several examples.

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