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arXiv · 2303.12825

Single-parameter variational wavefunctions for quantum Hall bilayers

Qi Hu·Titus Neupert·Glenn Wagner
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Abstract

Bilayer quantum Hall states have been shown to be described by a BCS-paired state of composite fermions. However, finding a qualitatively accurate model state valid across all values of the bilayer separation is challenging. Here, we introduce two variational wavefunctions, each with a single variational parameter, which can be thought of as a proxy for the BCS order parameter. Studying systems of up to 9+9 electrons in a spherical geometry using Monte Carlo methods, we show that the ground state can be accurately described by these single-parameter variational states. In addition, for the first time we provide a numerically exact wavefunction for the Halperin-111 state in terms of composite fermions.

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Qi Hu, Titus Neupert, Glenn Wagner. 2023-03-22. Single-parameter variational wavefunctions for quantum Hall bilayers. https://doi.org/10.1103/physrevb.109.155138

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