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

Łydżba, Patrycja; Jacak, Janusz

doi:10.1088/1361-648x/aad653

Cited by 5 publications

(4 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a result, in our Monte Carlo simulations, we identify a relative decrease of

⟨ {\overset{V}{true}}_{e e} ⟩

with a relative change of electron‐electron interactions compared to background‐background interactions. Furthermore, these conclusions concerning the expected potential energy,

⟨ \hat{V} ⟩

, agree with results from Monte Carlo simulations and exact diagonalizations available in the literature . What is more, they also imply that more stable quantum Hall states (which correspond to very robust plateaus in transport measurements resistant to changes of a disorder level, a dielectric constant or a temperature) are characterized by weaker correlations.…”

Section: Verification In Quantum Hall Regime: Laughlin's Hierarchysupporting

confidence: 85%

“…If these enhanced dimensions allow a

1false q

‐loop cyclotron orbit to fit into the interparticle distance ( q is an odd number), an exchange path is built from its half‐piece and comprises

\frac{q - 1}{2}

supplementary loops (

q - 1

has to be even; this ensures that an exchange path remains open). The above considerations can be utilized to put forward commensurability conditions, which determine a hierarchy of possible quantum Hall fluids,

\begin{matrix} true \\ right \frac{B S}{ϕ_{0} N} = \sum_{ζ = 1}^{m - 1} (β_{ζ} \frac{α_{ζ}}{a_{ζ}}) + β_{x} \frac{1}{x} \leftrightarrow ν = \frac{1}{0true \sum_{ζ = 1}^{m - 1} ((), β_{ζ}, \frac{α_{ζ}}{a_{ζ}}) + β_{x} \frac{1}{x}}, \end{matrix}

where

0true \sum_{ζ = 1}^{m - 1} (α_{ζ}) + 1 = q

. Furthermore, all α are even numbers, a and x are integers, while

β = \pm 1

.…”

Section: Verification In Quantum Hall Regime: Beyond Laughlin's Hieramentioning

confidence: 99%

See 1 more Smart Citation

Identifying Particle Correlations in Quantum Hall Regime

Łydżba

Jacak

2017

Annalen der Physik

View full text Add to dashboard Cite

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.

show abstract

“…As a result, in our Monte Carlo simulations, we identify a relative decrease of

⟨ {\overset{V}{true}}_{e e} ⟩

with a relative change of electron‐electron interactions compared to background‐background interactions. Furthermore, these conclusions concerning the expected potential energy,

⟨ \hat{V} ⟩

Section: Verification In Quantum Hall Regime: Laughlin's Hierarchysupporting

confidence: 85%

“…If these enhanced dimensions allow a

1false q

‐loop cyclotron orbit to fit into the interparticle distance ( q is an odd number), an exchange path is built from its half‐piece and comprises

\frac{q - 1}{2}

supplementary loops (

q - 1

\begin{matrix} true \\ right \frac{B S}{ϕ_{0} N} = \sum_{ζ = 1}^{m - 1} (β_{ζ} \frac{α_{ζ}}{a_{ζ}}) + β_{x} \frac{1}{x} \leftrightarrow ν = \frac{1}{0true \sum_{ζ = 1}^{m - 1} ((), β_{ζ}, \frac{α_{ζ}}{a_{ζ}}) + β_{x} \frac{1}{x}}, \end{matrix}

where

0true \sum_{ζ = 1}^{m - 1} (α_{ζ}) + 1 = q

. Furthermore, all α are even numbers, a and x are integers, while

β = \pm 1

.…”

Section: Verification In Quantum Hall Regime: Beyond Laughlin's Hieramentioning

confidence: 99%

Identifying Particle Correlations in Quantum Hall Regime

Łydżba

Jacak

2017

Annalen der Physik

View full text Add to dashboard Cite

show abstract

“…The construction of the trial wave function in the CF model is thus inaccurate because the projection onto LLL violates in an uncontrolled manner the symmetry of the multiparticle wave function, which must comply with the structure of the cyclotron subgroup generators corresponding to the particular homotopy invariant ( 4 ) and to scalar unitary representation of these generators (the violation of the symmetry in CF wave functions has been demonstrated in [ 39 ]). The unitary representation of the cyclotron braid subgroup must be a projective representation of the full covering braid group adjusted to original electrons,

.…”

Section: Topological Invariants In 2d Systems Of Interacting Electrons In Magnetic Fieldmentioning

confidence: 99%

Limits of Applicability of the Composite Fermion Model

Jacak

2021

Materials

View full text Add to dashboard Cite

The popular model of composite fermions, proposed in order to rationalize FQHE, were insufficient in view of recent experimental observations in graphene monolayer and bilayer, in higher Landau levels in GaAs and in so-called enigmatic FQHE states in the lowest Landau level of GaAs. The specific FQHE hierarchy in double Hall systems of GaAs 2DES and graphene also cannot be explained in the framework of composite fermions. We identify the limits of the usability of the composite fermion model by means of topological methods, which elucidate the phenomenological assumptions in composite fermion structure and admit further development of FQHE understanding. We demonstrate how to generalize these ideas in order to explain experimentally observed FQHE phenomena, going beyond the explanation ability of the conventional composite fermion model.

show abstract

“…A distributional approach [15] for the one-dimensional hydrogen atom was developed. The integral equations technique can be effectively applied to the various problems of quantum mechanics [16][17][18]. The papers [19][20][21][22][23][24][25][26][27] can also enable one to become acquainted with the results obtained in this field.…”

Section: Introductionmentioning

confidence: 99%

Solving a singular integral equation for the one-dimensional Coulomb problem

2023

View full text Add to dashboard Cite

A new integral equation that describes the behavior of the momentum space wave function for the one-dimensional Coulomb potential is proposed. The obtained result turned out to be a homogeneous Fredholm integral equation of the second kind and a singular integral equation, because its kernel has a singularity at some point in the momentum space. A nontriviality of the method of solving this singular integral equation lies in the application of the integral representation for its integral kernel. The technique applied in this paper made it possible to show that the wave function in the momentum representation is simultaneously a solution of the homogeneous Fredholm integral equation of the second kind and of the linear Volterra integral equation of the second kind. Since a linear Volterra integral equation of the second kind was easily transformed into a second order linearinhomogeneous differential equation with constant coefficients, the eigenfunctions and eigenvalues in the one-dimensional Coulomb problem were found without any difficulties. Such a circumstance may indicate the validity of the new integral equation and the proposed method of its solving.

show abstract

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

Cited by 5 publications

References 59 publications

Identifying Particle Correlations in Quantum Hall Regime

Identifying Particle Correlations in Quantum Hall Regime

Limits of Applicability of the Composite Fermion Model

Solving a singular integral equation for the one-dimensional Coulomb problem

Contact Info

Product

Resources

About