Half-Filled Lowest Landau Level on a Thin Torus

Bergholtz, Emil J.; Karlhede, A.

doi:10.1103/physrevlett.94.026802

Cited by 123 publications

(206 citation statements)

References 23 publications

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“…A similar story has been discussed in an isotropic FQH system with extreme geometry, such as in a thin torus or a cylinder limit, [22][23][24] and in a recent work 25 on the graphene ribbon with flat bands. They can be explained under the same principle in Ref.…”

Section: -4mentioning

confidence: 93%

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Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions

et al. 2012

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We study the anisotropic effect of the Coulomb interaction on a 1/3-filling fractional quantum Hall system by using an exact diagonalization method on small systems in torus geometry. For weak anisotropy the system remains to be an incompressible quantum liquid, although anisotropy manifests itself in density correlation functions and excitation spectra. When the strength of anisotropy increases, we find the system develops a Hallsmectic-like phase with a one-dimensional charge density wave order and is unstable towards the one-dimensional crystal in the strong anisotropy limit. In all three phases of the Laughlin liquid, Hall-smectic-like, and crystal phases the ground state of the anisotropic Coulomb system can be well described by a family of model wave functions generated by an anisotropic projection Hamiltonian. We discuss the relevance of the results to the geometrical description of fractional quantum Hall states proposed by Haldane [Phys. Rev. Lett. 107, 116801 (2011)].

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Section: -4mentioning

confidence: 93%

“…They can be explained under the same principle in Ref. 24 by a sorting Hamiltonian. When the interaction anisotropy increases, the repulsion-related diagonal terms dominate, which has the similar effect as geometry on the isotropic FQH and as the local orbital expansion on the flat-band graphene ribbon.…”

Section: -4mentioning

confidence: 99%

Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions

et al. 2012

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“…In the thin-torus limit L 2 ≪ 1 or κ ≫ 1, the overlap between two adjacent Landau orbitals is negligible, thus the system can be viewed as a one-dimensional chain. Because the magnitude of U σσ ′ r,s ∝ e −κ 2 (s 2 +r 2 )/2 decays exponentially when κ → ∞, the dominated interaction Hamiltonian in the thin-torus limit is 69,70 …”

Section: Effective Theory In the Thin-torus Limitmentioning

confidence: 99%

“…Here we analyze the degeneracy pattern of the edge excitation spectrum of the fermionic Moore-Read (MR) Pfaffian state. Our analysis is based on root configurations 68 on the sphere, which are also equivalent to configurations in the thin-torus limit 69,70 .…”

Section: Density-matrix Renormalization Groupmentioning

confidence: 99%

“…That is, we will derive an effective theory for the underlying quantum phase transition in the thin-torus limit 30,[68][69][70] . Unlike the effective edge theory, such kind of effective theory is constructed for the bulk and is expected to describe how the ground-state manifold evolves from the (331) degeneracy to the MR Pfaffian degeneracy.…”

Section: Effective Theory In the Thin-torus Limitmentioning

confidence: 99%

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Fractional quantum Hall bilayers at half filling: Tunneling-driven non-Abelian phase

et al. 2016

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Multicomponent quantum Hall systems with internal degrees of freedom provide a fertile ground for the emergence of exotic quantum liquids. Here we investigate the possibility of non-Abelian topological order in the half-filled fractional quantum Hall (FQH) bilayer system driven by the tunneling effect between two layers. By means of the state-of-the-art density-matrix renormalization group, we unveil "finger print" evidence of the non-Abelian Moore-Read Pfaffian state emerging in the intermediate-tunneling regime, including the ground-state degeneracy on the torus geometry and the topological entanglement spectroscopy (entanglement spectrum and topological entanglement entropy) on the spherical geometry, respectively. Remarkably, the phase transition from the previously identified Abelian (331) Halperin state to the non-Abelian Moore-Read Pfaffian state is determined to be continuous, which is signaled by the continuous evolution of the universal part of the entanglement spectrum, and discontinuities in the excitation gap and the derivative of the ground-state energy. Our results not only provide a "proof-of-principle" demonstration of realizing a non-Abelian state through coupling different degrees of freedom, but also open up a possibility in FQH bilayer systems for detecting different chiral p−wave pairing states.

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A Simple View on the Quantum Hall System

Bergholtz

Karlhede

2008

NATO Science for Peace and Security Series B: Physics and Biophysics

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Half-Filled Lowest Landau Level on a Thin Torus

Cited by 123 publications

References 23 publications

Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions

Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions

Fractional quantum Hall bilayers at half filling: Tunneling-driven non-Abelian phase

A Simple View on the Quantum Hall System

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