Natural orbitals and their occupation numbers for free anyons in the magnetic gauge

Jerzy Cioslowski; Oliver M Brown; Tomasz Maciazek

doi:10.1103/PhysRevA.109.023316

Natural orbitals and their occupation numbers for free anyons in the magnetic gauge

Jerzy Cioslowski
, Oliver M Brown
, Tomasz Maciazek

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

1 Citation (Scopus)

Abstract

We investigate the properties of natural orbitals and their occupation numbers of the ground state of two noninteracting anyons characterized by the fractional statistics parameter α and confined in a harmonic trap. We work in the boson magnetic gauge where the anyons are modeled as composite bosons with magnetic flux quanta attached to their positions. We derive an asymptotic form of the weakly occupied natural orbitals, and show that their corresponding (ordered descendingly) occupation numbers decay according to the power law n^(−(4+2α)), where n is the index of the natural orbital. We find remarkable numerical agreement of the theory with the natural orbitals and their occupation numbers computed from the spectral decomposition of the system's wave function. We explain that the same results apply to the fermion magnetic gauge.

Original language	English
Article number	023316
Number of pages	10
Journal	Physical Review A
Volume	109
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevA.109.023316
Publication status	Published - 9 Feb 2024

Bibliographical note

Funding Information:
The authors would like to thank Jonathan Robbins for helpful discussions. The numerical computations presented here were conducted using the University of Bristol HPC system (BlueCrystal 4). The research described in this publication has been funded by the National Science Center (Poland) under Grant No. 2022/47/B/ST4/00002. The support from Max-Planck-Institut für Physik komplexer Systeme (MPI PKS), Dresden, is also acknowledged by one of the authors (J.C.).

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© 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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title = "Natural orbitals and their occupation numbers for free anyons in the magnetic gauge",

abstract = "We investigate the properties of natural orbitals and their occupation numbers of the ground state of two noninteracting anyons characterized by the fractional statistics parameter α and confined in a harmonic trap. We work in the boson magnetic gauge where the anyons are modeled as composite bosons with magnetic flux quanta attached to their positions. We derive an asymptotic form of the weakly occupied natural orbitals, and show that their corresponding (ordered descendingly) occupation numbers decay according to the power law n\textasciicircum{}(−(4+2α)), where n is the index of the natural orbital. We find remarkable numerical agreement of the theory with the natural orbitals and their occupation numbers computed from the spectral decomposition of the system's wave function. We explain that the same results apply to the fermion magnetic gauge.",

author = "Jerzy Cioslowski and Brown, \{Oliver M\} and Tomasz Maciazek",

note = "Funding Information: The authors would like to thank Jonathan Robbins for helpful discussions. The numerical computations presented here were conducted using the University of Bristol HPC system (BlueCrystal 4). The research described in this publication has been funded by the National Science Center (Poland) under Grant No. 2022/47/B/ST4/00002. The support from Max-Planck-Institut f{\"u}r Physik komplexer Systeme (MPI PKS), Dresden, is also acknowledged by one of the authors (J.C.). Publisher Copyright: {\textcopyright} 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the {"}https://creativecommons.org/licenses/by/4.0/{"}Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.",

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TY - JOUR

T1 - Natural orbitals and their occupation numbers for free anyons in the magnetic gauge

AU - Cioslowski, Jerzy

AU - Brown, Oliver M

AU - Maciazek, Tomasz

N1 - Funding Information: The authors would like to thank Jonathan Robbins for helpful discussions. The numerical computations presented here were conducted using the University of Bristol HPC system (BlueCrystal 4). The research described in this publication has been funded by the National Science Center (Poland) under Grant No. 2022/47/B/ST4/00002. The support from Max-Planck-Institut für Physik komplexer Systeme (MPI PKS), Dresden, is also acknowledged by one of the authors (J.C.). Publisher Copyright: © 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

PY - 2024/2/9

Y1 - 2024/2/9

N2 - We investigate the properties of natural orbitals and their occupation numbers of the ground state of two noninteracting anyons characterized by the fractional statistics parameter α and confined in a harmonic trap. We work in the boson magnetic gauge where the anyons are modeled as composite bosons with magnetic flux quanta attached to their positions. We derive an asymptotic form of the weakly occupied natural orbitals, and show that their corresponding (ordered descendingly) occupation numbers decay according to the power law n^(−(4+2α)), where n is the index of the natural orbital. We find remarkable numerical agreement of the theory with the natural orbitals and their occupation numbers computed from the spectral decomposition of the system's wave function. We explain that the same results apply to the fermion magnetic gauge.

AB - We investigate the properties of natural orbitals and their occupation numbers of the ground state of two noninteracting anyons characterized by the fractional statistics parameter α and confined in a harmonic trap. We work in the boson magnetic gauge where the anyons are modeled as composite bosons with magnetic flux quanta attached to their positions. We derive an asymptotic form of the weakly occupied natural orbitals, and show that their corresponding (ordered descendingly) occupation numbers decay according to the power law n^(−(4+2α)), where n is the index of the natural orbital. We find remarkable numerical agreement of the theory with the natural orbitals and their occupation numbers computed from the spectral decomposition of the system's wave function. We explain that the same results apply to the fermion magnetic gauge.

U2 - 10.1103/PhysRevA.109.023316

DO - 10.1103/PhysRevA.109.023316

M3 - Article (Academic Journal)

SN - 2469-9926

VL - 109

JO - Physical Review A

JF - Physical Review A

IS - 2

M1 - 023316

ER -

Natural orbitals and their occupation numbers for free anyons in the magnetic gauge

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