Edge-mode velocities and thermal coherence of quantum Hall interferometers

Hu, Zi-Xiang; Rezayi, E. H.; Wan, Xin; Yang, Kun

doi:10.1103/physrevb.80.235330

Cited by 48 publications

(54 citation statements)

References 52 publications

(112 reference statements)

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“…Entanglement spectrum gives not only the characteristic degeneracy pattern of the edge excitation, but also the edgemode velocity 82 . In the conformal field theory, the edge-mode of the Laughlin state is described by a single branch of chiral charged bosons.…”

Section: Summary and Discussionmentioning

confidence: 99%

Chiral and critical spin liquids in a spin-12kagome antiferromagnet

2015

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The kagome spin-1/2 systems have attracted intensive attentions in recent years as the primary candidate for hosting different gapped spin liquids (SL). To uncover the nature of the novel quantum phase transition between the SL states, we study a minimum XY model with the nearest neighbor (NN) (Jxy), the second and third NN couplings (J2xy = J3xy = J ′ xy ). We identify the time reversal symmetry broken chiral SL (CSL) with the turn on of a small perturbation J ′ xy ∼ 0.06Jxy, which is fully characterized by the fractionally quantized topological Chern number and the conformal edge spectrum as the ν = 1/2 fractional quantum Hall state. Interestingly, the NN XY model (J ′ xy = 0) is shown to be a critical SL state adjacent to the CSL, characterized by the gapless spin singlet and spin triplet excitations. The quantum phase transition from the CSL to the gapless critical SL is driven by the collapsing of the neutral (spin singlet) excitation gap. The effect of the NN spin-z coupling Jz is also studied, which leads to a quantum phase diagram with an extended regime for the gapless SL.

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Section: Summary and Discussionmentioning

confidence: 99%

Chiral and critical spin liquids in a spin-12kagome antiferromagnet

2015

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“…(24,25). For better precision for this small number of particles, we also take into account the next-to-leading order in variation with N in Eqs.…”

Section: Measuring Scaling Dimensions By a Monte-carlo Methodsmentioning

confidence: 99%

“…For better precision for this small number of particles, we also take into account the next-to-leading order in variation with N in Eqs. (24,25). At fixed L and fixed value of the confining potential β, the velocities v c and v n scale as N because the slope of the parabolic confining potential at the position of the edge grows like N at leading order.…”

Section: Measuring Scaling Dimensions By a Monte-carlo Methodsmentioning

confidence: 99%

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Many-body study of a quantum point contact in the fractional quantum Hall regime atν=5/2

2013

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We study a quantum point contact in the fractional quantum Hall regime at Landau level filling factors ν = 1/3 and ν = 5/2. By using exact diagonalizations in the cylinder geometry we identify the edge modes in the presence of a parabolic confining potential. By changing the sign of the potential we can access both the tunneling through the bulk of the fluid and the tunneling between spatially separated droplets. This geometry is realized in the quantum point contact geometry for two-dimensional electron gases. In the case of the model Moore-Read Pfaffian state at filling factor ν = 5/2 we identify the conformal towers of many-body eigenstates including the non-Abelian sector. By a Monte-Carlo technique we compute the various scaling exponents that characterize the edge modes. In the case of hard-core interactions whose ground states are exact model wavefunction we find equality of neutral and charged velocities for the Pfaffian state both bosonic and fermionic.

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“…For regular computing systems, the main bottleneck of this method for large systems is the large storage space (or memory) for the edge Jacks. [34]. E 0 ( M) is the lowest eigenenergy for the given momentum M. Through finite-size scaling we can extrapolate the edge-mode velocities in the thermodynamic limit.…”

Section: A Diagonalization In the Truncated Space Of Edge Statesmentioning

confidence: 99%

Construction of edge states in fractional quantum Hall systems by Jack polynomials

Lee

Wan

2014

Phys. Rev. B

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We study the edge-mode excitations of a fractional quantum Hall droplet by expressing the edge-state wave functions as linear combinations of Jack polynomials with a negative parameter. We show that the exact diagonalization within a subspace of Jack polynomials can be used to generate the chiral edge-mode excitation spectrum in the Laughlin phase and the Moore-Read phase with realistic Coulomb interaction. The truncation technique for the edge excitations simplifies the procedure to reliably extract the edge-mode velocities, which avoids the otherwise complicated analysis of the full spectrum that contains both edge and bulk excitations. Generalization to the Read-Rezayi state is also discussed.

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Edge-mode velocities and thermal coherence of quantum Hall interferometers

Cited by 48 publications

References 52 publications

Chiral and critical spin liquids in a spin-12kagome antiferromagnet

Chiral and critical spin liquids in a spin-12kagome antiferromagnet

Many-body study of a quantum point contact in the fractional quantum Hall regime atν=5/2

Construction of edge states in fractional quantum Hall systems by Jack polynomials

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