17 September 2020 Thu 4 pm

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Fractional quantum Hall (FQH) effect is one of the striking phenomena of low-dimensional condensed matter systems. This is yet not been understood completely from many-prospectives such as the occurrence of conductivity plateau at a certain fraction of electron density at the Landau level. The exact analytic solution for the ground-state wave function describing such a system is quite challenging due to the presence long-range interactions among the particles. In this context, conformal field theory (CFT) has turned out to be an interesting tool to study such quantum many-body systems proficiently. Due to the inbuilt long-range properties of the Hamiltonian derived within the framework of CFT, these models are very challenging to realize in experiments. Therefore, it is always beneficial to construct a local model from these non-local ones without losing much of the physics. In this talk, I will discuss different strategies to find out suitable local models from these long-ranged models on different lattice geometries involving hard-core bosons and spinless fermions at certain filling fractions. I will also compare results obtained using local models with the non-local one for a better understanding of our constructed local Hamiltonians. Finally, I will briefly mention some dynamical aspects of our derived long-ranged models for a square lattice.   

References:

1.  A. E. B. Nielsen, G. Sierra, and J. I. Cirac, Nat. Commun. 4, 2864 (2013)

2.  Dillip K Nandy, N. S. Srivatsa, and Anne E. B. Nielsen, Phys. Rev. B 100, 035123 (2019)

3.  Dillip K. Nandy, N. S. Srivatsa, and Anne E. B. Nielsen, Local Hamiltonians for one-dimensional critical models, 

     J. Stat. Mech. (2018) 063107

4.  A. E. B. Nielsen, G. Sierra, and J. I. Cirac, Nat. Commun. 4, 2864 (2013)