Pair-Distribution Functions of Laughlin Quasielectrons in Partially Filled Composite Fermion Levels

Wodziński, D.; Wójs, Arkadiusz; Quinn, John J.

doi:10.12693/aphyspola.108.909

Cited by 2 publications

(2 citation statements)

References 16 publications

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“…However, one interesting feature can be observed for all enigmatic filling factors-a shoulder, which is especially pronounced for systems composed of less than 50 particles. This plateaulike peculiarity has already been noticed in diagonalization studies for ν = 4 11 and systems comprising up to 14 particles [52]. However, simulations were performed in a correlated CF basis and only quasi-particles from a partially filled quasi-particle level were taken into account; and all quasiparticles from completely filled quasi-particle levels were disregarded.…”

Section: Pair Distribution Functionmentioning

confidence: 66%

Many-body wave functions for correlated systems in magnetic fields: Monte Carlo simulations in the lowest Landau level

Łydżba

Jacak²

2018

J. Phys.: Condens. Matter

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We put forward possible wave functions for quantum Hall states in the lowest Landau level. These were deduced from the topological approach based on the relation between braid groups and the quantum statistics, as well as the commensurability condition unavoidable for collective states in magnetic fields. In this paper we demonstrate that the [Formula: see text]-field imposes restrictions on braid trajectories (i.e. elements of the full braid group). This results in the appearance of cyclotron subgroups, instead of the full braid group, for certain filling factors. The fermion representation of cyclotron subgroups defines transformations of wave functions in the quantum Hall regime. Hence, it sets quantum statistics (transformations of [Formula: see text] under exchanges of arguments), which is unavoidable for collective states (in compliance with the framework of Feynman's path integrals). Finally, the topological approach allows to define the hierarchy of fillings in the lowest Landau level, which agree with the hierarchy observed in quantum Hall devices (i.e. in transport measurements). The symmetry of a many-body wave function (i.e. quantum statistics) is always determined by a 1D unitary representation of the system's braid group. Using this topologically-originated property, we demonstrate that many-body wave functions for selected fillings of the lowest Landau level may not be purely antisymmetric. Only systems composed of fermions are investigated. Additionally, we present Monte Carlo calculations in a disc geometry, which remain in a nice agreement with predictions of exact diagonalizations (expected values of potential energy and pair distribution functions are presented). No boundary potential is assumed.

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Section: Pair Distribution Functionmentioning

confidence: 66%

Many-body wave functions for correlated systems in magnetic fields: Monte Carlo simulations in the lowest Landau level

Łydżba

Jacak²

2018

J. Phys.: Condens. Matter

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“…An investigation of various correlation functions is generally time‐consuming (especially for systems comprising tens of particles). Therefore, only a pair distribution function,

g_{2} false(boldr false)

, is commonly studied in the papers . Furthermore, signs of the solid‐like local order are already visible in this two‐body function.…”

Section: Combined Simulated Annealing and Artificial Distribution Methodsmentioning

confidence: 99%

Identifying Particle Correlations in Quantum Hall Regime

Łydżba

Jacak

2017

Annalen der Physik

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We introduce a method that allows the disclosure of correlations between particle positions in an arbitrary many-body system. The method is based on a well-known simulated annealing algorithm and the proposed artificial distribution technique. Additionally, we investigate correlations in quantum Hall liquids (we consider many-body wave functions that have been recently determined via the cyclotron subgroup model) and present three-dimensional plots of configuration probability distributions that have been established from numerical simulations. We demonstrate that the preferred simultaneous positions of particles (configurations of positions, which correspond to large values of a system's probability distribution, | N | 2 ) tend to form complicated geometric structures, which are equivalent to classical Wigner crystals only for Laughlin states. Furthermore, we claim that quantum Hall liquids attributed to non-Laughlin fillings are correlated on subdomains rather than on a whole particle domain (due to a quantizing magnetic field, which modifies the topology of a system's dynamics). Finally, we characterize Hall-like internal orders in terms of statistical correlations (one-dimensional unitary representations of cyclotron subgroups). Our conclusions concerning the stability of many-body states agree with transport measurements and various numerical studies.

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Pair-Distribution Functions of Laughlin Quasielectrons in Partially Filled Composite Fermion Levels

Cited by 2 publications

References 16 publications

Many-body wave functions for correlated systems in magnetic fields: Monte Carlo simulations in the lowest Landau level

Many-body wave functions for correlated systems in magnetic fields: Monte Carlo simulations in the lowest Landau level

Identifying Particle Correlations in Quantum Hall Regime

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