The Density Profile of the Laughlin Wave Function of Fractional Quantum Hall Effect

by Mr Gabriel Cardoso (Stony Brook University)

Friday 25 Feb 2022, 10:00 → 11:00 Asia/Shanghai

ONLINE

Abstract

Similarly to the case of anomalous Hall effect, the fractional quantum Hall effect (FQHE) is explained by the consequences of non-trivial topology in the charge transport. However, the system is now very different, and in fact much more complicated, because of the presence of strong interactions. Momentous progress was achieved by Laughlin when he proposed an ansatz for the wave function of the lowest Landau level at odd fractional filling by using a plasma analogy [1]. In this talk, I will show how one can explore this analogy further to explain non-perturbative boundary properties of the Laughlin state through the phase diagram of the two-dimensional one-component plasma (2DOCP). By using a combination of analytical and computational methods, we show the existence of a surface phase transition in the plasma which we name “Freezing at the Edge” [2]. If time permits, I will also comment on the relationship of this problem to the quantization of two-dimensional hydrodynamics [3, 4].

[1] R. B. Laughlin, “Anomalous quantum hall effect: an incompressible quantum fluid with fractionally charged excitations,” Physical Review Letters, vol. 50, no. 18, p. 1395, 1983.
[2] G.  Cardoso, J.-M.  St´ephan, and A.  G.  Abanov, “The boundary density profile of a coulomb droplet. freezing at the edge,” Journal of Physics A: Mathematical and Theoretical, vol. 54, no. 1, p. 015002, 2020.
[3] D. S. Berman and G. Cardoso, “Geometric quantization: Particles, fields and strings,” arXiv preprint arXiv:2201.00349, 2022.
[4] P. Wiegmann, “Quantum hydrodynamics, rotating superfluid and gravitational anomaly,” Journal of Experimental and Theoretical Physics, vol. 129, no. 4, pp. 642–650, 2019.

Biography

Gabriel received his undergraduate degree from the Federal University of Parana (Brazil) and Queen Mary University of London (UK) in 2017. Since then, he has been working towards a PhD at Stony Brook University (USA) with Alexander G. Abanov (Simons Center from Geometry and Physics) in the field of topological phases of matter. His works focus on geometrical and non-perturbative properties of these phases as well as their practical applications in quantum computation.

Division

Condensed Matter

Other information

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