Holography of the lowest Landau level problem
Ajay Mohan (TIFR Mumbai)
We consider a system of fermions on a 2 dimensional plane with a perpendicular magnetic field (also called the Landau problem) whose spectrum is labelled by Landau levels. While it is well-known that there is a classical description of the lowest Landau level in terms of an effectively 1 dimensional constrained system, our recent findings suggest that this 1D-2D correspondence holds quantum-mechanically as well. Moreover, we find to our surprise that while certain physical quantities of the original 2D theory have a description in terms of an equivalent 1D theory (like the 2D fermion density of an N-fermion state), certain other quantities (like the ground state entanglement entropy) partially remember the 2D origin of the system. In this talk, I will present these findings in detail.