Programme

P.6 -- Poster, ANSWCCMS-2023

Date: Tuesday, 7 November 2023

Time: 13:00 - 14:30

Lattice Laughlin Quasiparticles

Aniket Patra

Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon, Korea

Use of trial wavefunctions to explain fractional quantum Hall effect (FQHE) was pioneered by Robert Laughlin (1998 Nobel prize in physics). This ansatz wavefunction itself possesses fascinating topological properties. In this talk, we consider several states on lattices, that have fractionally quantized Hall conductivities. We propose ans ̈aze for these states and their topological excitations. In the continuum limit, one of these trial wavefunctions becomes the celebrated Laughlin ansatz for FQHE with filling factor 1/q. First, we analyze the Laughlin quasielectron. The existing trial wavefunctions of the quasielectron have several problems, such as lack of screening or wrong braiding properties. It was shown, however, that for lattice fractional quantum Hall systems, it is possible to find a relatively simple quasielectron wavefunction that has all the desired properties [1]. This naturally poses the question: what happens to this wavefunction in the continuum limit? Our analysis demonstrates that in general the continuum limit of the lattice Laughlin quasielectron does not exist. We hence conclude that the lattice quasielectron wavefunction does not solve the difficulty of finding good trial states for quasielectrons in the continuum [2]. Next, we consider a lattice ansatz wavefunction (lattice Laughlin state in a plane with q = non-integer) corresponding to a system of multiple hardcore anyons [3]. The continuum limit of this wavefunction coincides with one of the states in the lowest Landau level ground state of the many-anyon continuum Hamiltonian, where hardcore anyons are considered as composites of hardcore bosons (fermions) and attached “statistical” point flux tubes. Finally, we show the existence of emergent quasiparticle (both hole and particle type) over this lattice many-anyon ground state. [1] A. E. B. Nielsen, I. Glasser, and I. D. Rodr ́ıguez, Quasielectrons as inverse quasiholes in lattice fractional quantum Hall models, New J. Phys. 20, 033029 (2018). [2] A. Patra, B. Hillebrecht, and A. E. B. Nielsen, Continuum limit of lattice quasielectron wavefunctions, J. Stat. Mech. 2021, 083101 (2021). [3] J. Wildeboer, A. Patra, S. Manna, and A. E. B. Nielsen, Anyonic quasiparticles of hardcore anyons, Phys. Rev. B 102, 125117 (2020)

Presenter: Aniket Patra