#### IMSc Webinar

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

#### Subhankar Khatua

##### The Institute of Mathematical Sciences

*Google meet link: meet.google.com/tky-cfvf-sij*

Emergence is a powerful notion in several areas of science. It describes the properties of a system that do not resemble the behaviour of its microscopic constituents. In this talk, we explore emergence in the context of quantum magnets --- we argue that a quantum magnet in the semiclassical low energy limit maps to a (quantum) particle moving on the space of classical configurations that minimize energy. In some systems, there are many such minimum-energy configurations that are related by symmetry. In such a case, the low energy mapping is to free particle motion. However, there are systems with many minimum-energy configurations that are not symmetry related ---- a situation that is called accidental degeneracy. Since the configurations are not symmetry-related, the system at low energies may select one particular configuration among all. This phenomenon is popularly known as `order by disorder' or state selection due to fluctuations. We argue that, in the effective low energy description, state selection manifests as particle localization at some point on the space of the minimum-energy configurations. We discuss precise mechanisms by which state selection occurs. We present two distinct selection mechanisms --- a) order by potential: the particle localizes at the minima of a potential that arises from the zero-point energy of quantum fluctuations, b) order by singularity: If the minimum-energy configurations' space self-intersects, the particle localizes at the point (region) of self-intersection (singularity). This occurs entirely due to the geometry of the space concerned and quantum interference of decaying modes at the singularity. Here, the localization does not require any binding potential. We also argue that order by singularity is a stronger effect than order by potential.

Refs.:

1) S. Khatua, R. Shankar, R. Ganesh, The quantum spin quadrumer, Phys. Rev. B 97, 054403(2018)

2) S. Khatua, D. Sen, R. Ganesh, Effective theories for quantum spin clusters: Geometric phases and state selection by singularity, Phys. Rev. B 100, 134411(2019)

3) S. Srinivasan, S. Khatua, G. Baskaran, R. Ganesh, Order by singularity in Kitaev clusters, Phys. Rev. Research 2, 023212(2020)

4) S. Khatua, S. Srinivasan and R. Ganesh, State selection in frustrated magnets: order by disorder and order by singularity, (arXiv:2011.11668, communicated with PRB)

Done