PIRSA:19080082

Video URL

https://pirsa.org/19080082

Order by Singularity

Ganesh, R. (2019). Order by Singularity. Perimeter Institute for Theoretical Physics. https://pirsa.org/19080082

Ganesh, Ramachandran. Order by Singularity. Perimeter Institute for Theoretical Physics, Aug. 15, 2019, https://pirsa.org/19080082 

          @misc{ scivideos_PIRSA:19080082,
            doi = {10.48660/19080082},
            url = {https://pirsa.org/19080082},
            author = {Ganesh, Ramachandran},
            keywords = {Quantum Matter},
            language = {en},
            title = {Order by Singularity},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2019},
            month = {aug},
            note = {PIRSA:19080082 see, \url{https://scivideos.org/pirsa/19080082}}
          }

Ramachandran Ganesh The Institute of Mathematical Sciences - Chennai

Talk numberPIRSA:19080082
DOI10.48660/19080082
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

We present a paradigm for effective descriptions of quantum magnets. Typically, a magnet has many classical ground states — configurations of spins (as classical vectors) that have the least energy. The set of all such ground states forms an abstract space. Remarkably, the low energy physics of the quantum magnet maps to that of a single particle moving in this space.

This presents an elegant route to simulate simple quantum mechanical models using molecular magnets. For instance, a dimer coupled by an XY bond maps to a particle moving on a ring. An XY triangular magnet maps to a particle moving on two disjoint rings. We can even simulate Berry phases; when the spin has half-integer values, the particle sees a pi-flux  threaded through the rings.

A particularly interesting example is the XY tetrahedral magnet. Here, the ground state space is a 'non-manifold' due to singularities. These singularities behave like strong impurities to create bound states. The entire low energy physics of the magnet is dominated by these bound states. We call this phenomenon 'order by singularity’. This leads to a preference for certain classical ground states purely due to topology, rather than due to thermal or quantum fluctuations. Unlike order-by-disorder, this effect persists even in the classical limit.