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Melik-Alaverdian, V.; Ortíz, Gerardo; Bonesteel, N. E.

doi:10.1023/a:1010326231389

Cited by 10 publications

(10 citation statements)

References 17 publications

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“…Another possible extension of our work is the realization of the simulation of the full anyonic plasma on the sphere taking care appropriately of the fractional statistics and the phase factors to append to each disconnected region of the path integral expression for the partition function. This could become important in a study of the quantum Hall effect by placing a magnetic Dirac monopole at the center of the sphere 13,14 . Also the adaptation of our study to a fully relativistic Hamiltonian could be of some interest for the treatment of the Dirac points graphinos.…”

Section: Discussionmentioning

confidence: 99%

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One-component fermion plasma on a sphere at finite temperature

Fantoni

2018

Int. J. Mod. Phys. C

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We study through a computer experiment, using the restricted path integral Monte Carlo method, a onecomponent fermion plasma on a sphere at finite, non-zero, temperature. We extract thermodynamic properties like the kinetic and internal energy per particle and structural properties like the radial distribution function. This study could be relevant for the characterization and better understanding of the electronic properties of hollow graphene spheres.

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Section: Discussionmentioning

confidence: 99%

“…A quantum fluid on a Riemannian surface has been studied before in relation to the quantum Hall effect [10][11][12] . A generalized stochastic method has also been implemented for the many-body ground state 13,14 . We are not aware of any path integral Monte Carlo attempt in the spirit of our work.…”

Section: Introductionmentioning

confidence: 99%

One-component fermion plasma on a sphere at finite temperature

Fantoni

2018

Int. J. Mod. Phys. C

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“…For electrons in a magnetic field, the wave function is necessarily complex, but Ortiz, Ceperley and Martin 27 developed a fixed phase DMC in which one expresses the wave function as |Φ(R)|e iφ(R) (R represents the particle coordinates collectively), assumes the phase to be fixed, which can be incorporated into the Hamiltonian, and then determines the lowest energy state within the chosen phase sector. This method was generalized for spherical geometry by Melik-Alaverdian et al 28,30 .…”

Section: Fixed Phase Diffusion Monte Carlo Studymentioning

confidence: 99%

Surprising robustness of particle-hole symmetry for composite-fermion liquids

2017

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We report on fixed phase diffusion Monte Carlo calculations that show that, even for a large amount of Landau level mixing, the energies of the Pfaffian and anti-Pfaffian phases remain very nearly the same, as also do the excitation gaps at 1/3 and 2/3. These results, combined with previous theoretical and experimental investigations, indicate that particle hole (PH) symmetry for composite fermion states is much more robust than a priori expected, emerging even in models that explicitly break PH symmetry. We provide insight into this fact by showing that the low energy physics of a generic repulsive 3-body interaction is captured, to a large extent and over a range of filling factors, by a mean field approximation that maps it into a PH symmetric 2-body interaction. This explains why Landau level mixing, which effectively generates such a generic 3-body interaction, is inefficient in breaking PH symmetry. As a byproduct, our results provide a systematic construction of a 2-body interaction which produces, to a good approximation, the Pfaffian wave function as its ground state. I. BACKGROUND AND MOTIVATIONIt has been appreciated since the early 1980s that Landau level (LL) mixing leads to corrections in various observable quantities in fractional quantum Hall effect (FQHE), such as the transport gaps 1,2 . The effect of LL mixing is two-fold: it alters the 2-body interaction and also induces multi-particle interaction. While both lead to corrections, the latter also breaks the symmetry under particle-hole (PH) transformation, which is an exact symmetry for electrons confined to a single LL and interacting by a 2-body interaction, providing an exact relation between the wave functions and spectra at filling factors ν and 1 − ν.The issue of PH symmetry has received much attention in recent years, in the contexts of both the competition of the Moore-Read Pfaffian 3 (Pf) and the antiPfaffian 4,5 (APf) states for the ν = 5/2 FQHE 6-12 , and the composite-fermion (CF) Fermi sea at ν = 1/2 13-18 . A surprising message revealed by these studies is that the PH symmetry for CF liquids is much more robust than one might a priori anticipate, emerging even for Hamiltonians that explicitly break PH symmetry. Let us list some examples. (i) The most dominant PH symmetry breaking term induced by LL mixing is the 3-body interaction 6 . Ref.19 found, surprisingly, that even a pure 3-body interaction produces, for a broad range of parameters, the standard Jain CF states at ν = n/(2n±1) 20,21 , which satisfy PH symmetry to a very good approximation; this demonstrates an emergent PH symmetry in the ground state for a model Hamiltonian that explicitly breaks PH symmetry. (ii) An emergent PH symmetry was found also for spinful bosons in the lowest LL (LLL) interacting via the hard core interaction 22 ; a priori, a bosonic system is not expected to obey PH symmetry at all. (iii) Wang et al. 18 have demonstrated that the Halperin-Lee-Read theory of composite fermions produces results that are consistent with PH symmetry, even though the ...

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“…We study in this work the effect of LL mixing through the nonperturbative method of fixed-phase diffusion Monte Carlo calculations [25][26][27]. We focus here on the phase transitions between differently spin-polarized FQH states as a function of the Zeeman energy, which are an ideal testing ground for the role of LL mixing, both because a wealth of experimental information exists for the critical energies where such transitions occur [28][29][30][31][32][33][34][35][36][37][38][39][40], and because they depend sensitively on LL mixing [40,41].…”

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confidence: 99%

Landau-Level Mixing and Particle-Hole Symmetry Breaking for Spin Transitions in the Fractional Quantum Hall Effect

2016

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The spin transitions in the fractional quantum Hall effect provide a direct measure of the tiny energy differences between differently spin-polarized states and thereby serve as an extremely sensitive test of the quantitative accuracy of the theory of the fractional quantum Hall effect, and, in particular, of the role of Landau-level mixing in lifting the particle-hole symmetry. We report on an accurate quantitative study of this physics, evaluating the effect of Landau-level mixing in a nonperturbative manner using a fixed-phase diffusion Monte Carlo method. We find excellent agreement between our calculated critical Zeeman energies and the experimentally measured values. In particular, we find, as also do experiments, that the critical Zeeman energies for fractional quantum Hall states at filling factors ν=2-n/(2n±1) are significantly higher than those for ν=n/(2n±1), a quantitative signature of the lifting of particle-hole symmetry due to Landau-level mixing.

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Cited by 10 publications

References 17 publications

One-component fermion plasma on a sphere at finite temperature

One-component fermion plasma on a sphere at finite temperature

Surprising robustness of particle-hole symmetry for composite-fermion liquids

Landau-Level Mixing and Particle-Hole Symmetry Breaking for Spin Transitions in the Fractional Quantum Hall Effect

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