Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Phase-diagram study in the half-integral fractional quantum Hall effect

Gautam Dev, X. C. Xie, Bruce A. Mason

Published Apr 15, 1995• 1 citation
Publisher

Abstract

In this paper we study the phase diagram of the ground-state quantum numbers as functions of Haldane pseudopotential parameters ${\mathit{V}}_{0}$ and ${\mathit{V}}_{1}$, keeping all other ${\mathit{V}}_{\mathit{m}}$'s at their Coulomb values. We study filling factors 1/2 and 5/2, using a system of eight electrons on a sphere. It is known that the Coulomb ground state is not a spin singlet. In the phase diagram, however, we find that there is a comparatively large region of L=0, S=0 states not far from the Coulomb point. Modifications necessary for the ground state to be in this sector are discussed. Some of the L=0, S=0 states in the phase diagram are incompressible because they have significant overlaps with the hollow core state or with the composite fermion states, which are known to be imcompressible.

DOI
10.1103/physrevb.51.10905

Related papers

Connection between spin-singlet and hierarchical wave functions in the fractional quantum Hall effect

D. Yoshioka, Allan H. MacDonald, S. M. Girvin

We propose trial expressions for the many-body wave functions of the incompressible fluid states responsible for the fractional quantum Hall effect at filling factor $\ensuremath{\nu}$ not equal to $\frac{1}{m}$. For $\ensuremath{\nu}=\frac{q}{p}$, the wave functions are related to the wave functions for the total $S=0$ states of objects with spin $\frac{(q\ensuremath{-}1)}{2}$. In particular, for $\ensuremath{\nu}=\frac{2}{5}$ the wave function is related to the total $S=0$, $\ensuremath{\nu}=\frac{1}{2}$ hollow-core-model ground state recently discovered by Haldane and Rezayi.

Physical review. B, Condensed matter•Aug 15, 1988•68 citations

Integral and fractional quantum Hall Ising ferromagnets

Karel Výborný, Ondřej Čertı́k, Daniela Pfannkuche +3 more

We compare quantum Hall systems at filling factors $\ensuremath{\nu}=2$ to $\ensuremath{\nu}=\frac{2}{3}$ and $\frac{2}{5}$, corresponding to the exact filling of two lowest electron or composite fermion (CF) Landau levels. The two fractional states are examples of CF liquids with spin dynamics. There is a close analogy between the ferromagnetic (spin polarization $P=1$) and paramagnetic $(P=0)$ incompressible ground states that occur in all three systems in the limits of large and small Zeeman spin splitting. However, the excitation spectra are different. At $\ensuremath{\nu}=2$, we find spin domains at half-polarization $(P=\frac{1}{2})$, while antiferromagnetic order seems most favorable in the CF systems. The transition between $P=0$ and 1, as seen when, e.g., the magnetic field is tilted, is also studied by exact diagonalization in toroidal and spherical geometries. The essential role of an effective CF-CF interaction is discussed, and the experimentally observed incompressible half-polarized state is found in some models.

arXiv:cond-mat/0609756•Physical Review B•Jan 29, 2007•11 citations

Quantum Hall effect of two-component bosons at fractional and integral fillings

Ying-Hai Wu, Jainendra K. Jain

We investigate the feasibility of many candidate quantum Hall states for two-component bosons in the lowest Landau level. We identify interactions for which spin-singlet incompressible states occur at filling factors $\ensuremath{\nu}=2/3$, $4/5$, and $4/3$, and partially spin-polarized states at filling factors $3/4$ and $3/2$, where ``spin'' serves as a generic label for the two components. We study ground states, excitations, edge states, and entanglement spectrum for systems with up to 16 bosons and construct explicit trial wave functions to clarify the underlying physics. The composite fermion theory very accurately describes the ground states as well as excitations at $\ensuremath{\nu}=2/3$, $4/5$, and $3/4$, although it is less satisfactory for the $\ensuremath{\nu}=3/2$ state. For $\ensuremath{\nu}=4/3$ a ``non-Abelian spin-singlet'' state, which is the exact ground state of a three-body contact interaction, has been proposed to occur even for a two-body contact interaction; our trial wave functions are very accurate for the excitations of the three-body interaction, but they do not describe the excitations of the two-body interaction very well. Instead, we find that the $\ensuremath{\nu}=4/3$ state is more likely to be a spin-singlet state of reverse-flux-attached composite fermions at filling ${\ensuremath{\nu}}^{*}=4$. We also consider incompressible states at integral filling factors $\ensuremath{\nu}=1$ and 2. The incompressible state at $\ensuremath{\nu}=1$ is shown to be well described by the parton-based Jain spin-singlet wave function, and the incompressible state at $\ensuremath{\nu}=2$ as the spin-singlet state of reverse-flux-attached composite fermions at ${\ensuremath{\nu}}^{*}=2$, which provides an example of the bosonic integer topological phase.

arXiv:1304.7553•Physical Review B•Jun 24, 2013•79 citations

Half-integral spin-singlet quantum Hall effect

Lotfi Belkhir, Xiaofeng Wu, Jainendra K. Jain

We provide numerical evidence that the ground state of a short-range-interaction model at \ensuremath{\nu}=1/2 is incompressible and spin singlet for a wide range of repulsive interactions. Furthermore it is accurately described by a trial wave function studied earlier. For the Coulomb interaction we find that this wave function provides a good description of the lowest-lying spin-singlet state, and propose that fractional quantum Hall effect would occur at \ensuremath{\nu}=1/2 if this state became the global ground state. Some conclusions of an earlier paper are invalidated by the present numerical study of a larger system; these will be indicated.

arXiv:cond-mat/9310020•Physical review. B, Condensed matter•Nov 15, 1993•16 citations

Spin in fractional quantum Hall systems

K. Výborný

A system at filling factor 2/3 could be a candidate for a quantum Hall ferromagnet at integer filling factor of composite fermions. Using exact diagonalization with electrons on a torus we study the transition from the singlet ground state to the polarized ground state at this filling and look for signatures of quantum Hall ferromagnetism. Differences between the fractional and corresponding integer systems are emphasised. Most interestingly, we find around the transition a low excited half-polarized state which might become the ground state in the thermodynamical limit. We study its structure and compare it to the singlet and polarized ground states. A new interpretation of the singlet state is suggested and comparison of the filling factors 2/3 and 2/5 is presented. Adding magnetic inhomogeneities into the system we investigate the stability of all the three involved states and the tendency to build up domains like in conventional ferromagnets.

arXiv:cond-mat/0603451•Annalen der Physik•Nov 30, 2006•5 citations

Fractional Quantum Hall Effect of Hard-Core Bosons in Topological Flat Bands

Yi-Fei Wang, Zheng‐Cheng Gu, Chang-De Gong +1 more

Recent proposals of topological flat band models have provided a new route to realize the fractional quantum Hall effect without Landau levels. We study hard-core bosons with short-range interactions in two representative topological flat band models, one of which is the well-known Haldane model (but with different parameters). We demonstrate that fractional quantum Hall states emerge with signatures of an even number of quasidegenerate ground states on a torus and a robust spectrum gap separating these states from the higher energy spectrum. We also establish quantum phase diagrams for the filling factor 1/2 and illustrate quantum phase transitions to other competing symmetry-breaking phases.

arXiv:1103.1686•Physical Review Letters•Sep 30, 2011•319 citations
In this paper we study the phase diagram of the ground-state quantum numbers as functions of Haldane pseudopotential parameters V0{\mathit{V}}_{0}V0​ and V1{\mathit{V}}_{1}V1​, keeping all other Vm{\mathit{V}}_{\mathit{m}}Vm​'s at their Coulomb values. We study filling factors 1/2 and 5/2, using a system of eight electrons on a sphere. It is known that the Coulomb ground state is not a spin singlet. In the phase diagram, however, we find that there is a comparatively large region of L=0, S=0 states not far from the Coulomb point. Modifications necessary for the ground state to be in this sector are discussed. Some of the L=0, S=0 states in the phase diagram are incompressible because they have significant overlaps with the hollow core state or with the composite fermion states, which are known to be imcompressible.
We propose trial expressions for the many-body wave functions of the incompressible fluid states responsible for the fractional quantum Hall effect at filling factor $\ensuremath{\nu}$ not equal to 1m\frac{1}{m}m1​. For $\ensuremath{\nu}=\frac{q}{p}$, the wave functions are related to the wave functions for the total S=0S=0S=0 states of objects with spin $\frac{(q\ensuremath{-}1)}{2}$. In particular, for $\ensuremath{\nu}=\frac{2}{5}$ the wave function is related to the total S=0S=0S=0, $\ensuremath{\nu}=\frac{1}{2}$ hollow-core-model ground state recently discovered by Haldane and Rezayi.
We compare quantum Hall systems at filling factors $\ensuremath{\nu}=2$ to $\ensuremath{\nu}=\frac{2}{3}$ and 25\frac{2}{5}52​, corresponding to the exact filling of two lowest electron or composite fermion (CF) Landau levels. The two fractional states are examples of CF liquids with spin dynamics. There is a close analogy between the ferromagnetic (spin polarization P=1P=1P=1) and paramagnetic (P=0)(P=0)(P=0) incompressible ground states that occur in all three systems in the limits of large and small Zeeman spin splitting. However, the excitation spectra are different. At $\ensuremath{\nu}=2$, we find spin domains at half-polarization (P=12)(P=\frac{1}{2})(P=21​), while antiferromagnetic order seems most favorable in the CF systems. The transition between P=0P=0P=0 and 1, as seen when, e.g., the magnetic field is tilted, is also studied by exact diagonalization in toroidal and spherical geometries. The essential role of an effective CF-CF interaction is discussed, and the experimentally observed incompressible half-polarized state is found in some models.
We investigate the feasibility of many candidate quantum Hall states for two-component bosons in the lowest Landau level. We identify interactions for which spin-singlet incompressible states occur at filling factors $\ensuremath{\nu}=2/3$, 4/54/54/5, and 4/34/34/3, and partially spin-polarized states at filling factors 3/43/43/4 and 3/23/23/2, where ``spin'' serves as a generic label for the two components. We study ground states, excitations, edge states, and entanglement spectrum for systems with up to 16 bosons and construct explicit trial wave functions to clarify the underlying physics. The composite fermion theory very accurately describes the ground states as well as excitations at $\ensuremath{\nu}=2/3$, 4/54/54/5, and 3/43/43/4, although it is less satisfactory for the $\ensuremath{\nu}=3/2$ state. For $\ensuremath{\nu}=4/3$ a ``non-Abelian spin-singlet'' state, which is the exact ground state of a three-body contact interaction, has been proposed to occur even for a two-body contact interaction; our trial wave functions are very accurate for the excitations of the three-body interaction, but they do not describe the excitations of the two-body interaction very well. Instead, we find that the $\ensuremath{\nu}=4/3$ state is more likely to be a spin-singlet state of reverse-flux-attached composite fermions at filling ${\ensuremath{\nu}}^{*}=4$. We also consider incompressible states at integral filling factors $\ensuremath{\nu}=1$ and 2. The incompressible state at $\ensuremath{\nu}=1$ is shown to be well described by the parton-based Jain spin-singlet wave function, and the incompressible state at $\ensuremath{\nu}=2$ as the spin-singlet state of reverse-flux-attached composite fermions at ${\ensuremath{\nu}}^{*}=2$, which provides an example of the bosonic integer topological phase.
We provide numerical evidence that the ground state of a short-range-interaction model at \ensuremath{\nu}=1/2 is incompressible and spin singlet for a wide range of repulsive interactions. Furthermore it is accurately described by a trial wave function studied earlier. For the Coulomb interaction we find that this wave function provides a good description of the lowest-lying spin-singlet state, and propose that fractional quantum Hall effect would occur at \ensuremath{\nu}=1/2 if this state became the global ground state. Some conclusions of an earlier paper are invalidated by the present numerical study of a larger system; these will be indicated.
A system at filling factor 2/3 could be a candidate for a quantum Hall ferromagnet at integer filling factor of composite fermions. Using exact diagonalization with electrons on a torus we study the transition from the singlet ground state to the polarized ground state at this filling and look for signatures of quantum Hall ferromagnetism. Differences between the fractional and corresponding integer systems are emphasised. Most interestingly, we find around the transition a low excited half-polarized state which might become the ground state in the thermodynamical limit. We study its structure and compare it to the singlet and polarized ground states. A new interpretation of the singlet state is suggested and comparison of the filling factors 2/3 and 2/5 is presented. Adding magnetic inhomogeneities into the system we investigate the stability of all the three involved states and the tendency to build up domains like in conventional ferromagnets.
Recent proposals of topological flat band models have provided a new route to realize the fractional quantum Hall effect without Landau levels. We study hard-core bosons with short-range interactions in two representative topological flat band models, one of which is the well-known Haldane model (but with different parameters). We demonstrate that fractional quantum Hall states emerge with signatures of an even number of quasidegenerate ground states on a torus and a robust spectrum gap separating these states from the higher energy spectrum. We also establish quantum phase diagrams for the filling factor 1/2 and illustrate quantum phase transitions to other competing symmetry-breaking phases.