Incompressible Quantum Liquids and New Conservation Laws

Seidel, Alexander; Fu, Henry; Lee, Dung-Hai; Leinaas, Jon Magne; Moore, Joel E.

doi:10.1103/physrevlett.95.266405

Cited by 139 publications

(252 citation statements)

References 28 publications

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“…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%

“…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%

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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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Section: Density-matrix Renormalization Groupmentioning

confidence: 99%

Section: Effective Theory In the Thin-torus Limitmentioning

confidence: 99%

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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“…In the "thin-torus" limit [112][113][114] the cylinder is effectively a one-dimensional spin-full fermion chain, the ground states reduce to the "root configurations".…”

Section: A the Interlayer-pfaffian Statementioning

confidence: 99%

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

et al. 2015

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Bilayer quantum Hall systems, realized either in two separated wells or in the lowest two sub-bands of a wide quantum well, provide an experimentally realizable way to tune between competing quantum orders at the same filling fraction. Using newly developed density matrix renormalization group techniques combined with exact diagonalization, we return to the problem of quantum Hall bilayers at filling ν = 1/3 + 1/3. We first consider the Coulomb interaction at bilayer separation d, bilayer tunneling energy ∆SAS, and individual layer width w, where we find a phase diagram which includes three competing Abelian phases: a bilayer-Laughlin phase (two nearly decoupled ν = 1/3 layers); a bilayer-spin singlet phase; and a bilayer-symmetric phase. We also study the order of the transitions between these phases. A variety of non-Abelian phases have also been proposed for these systems. While absent in the simplest phase diagram, by slightly modifying the interlayer repulsion we find a robust non-Abelian phase which we identify as the "interlayer-Pfaffian" phase. In addition to non-Abelian statistics similar to the Moore-Read state, it exhibits a novel form of bilayer-spin charge separation. Our results suggest that ν = 1/3 + 1/3 systems merit further experimental study. CONTENTS

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“…The problem is then relegated to identifying all conformal field theories leading to permissible wave functions. On the other hand, it has recently become appreciated that a large class of trial wave functions can be characterized by simple sequences of integers, either through the thin torus limit and adiabatic continuity [4][5][6][7][8][9], or through Jack polynomials [10]. The patterns of integers associated with viable quantum Hall states are in turn subject to a number of consistency requirements, such as rotational invariance of the associated Jack polynomials, or constraints on the associated "patterns of zeros" studied in Ref.…”

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confidence: 99%

S-Duality Constraints on 1D Patterns Associated with Fractional Quantum Hall States

Seidel¹

2010

Phys. Rev. Lett.

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Using the modular invariance of the torus, constraints on the 1D patterns are derived that are associated with various fractional quantum Hall ground states, e.g. through the thin torus limit. In the simplest case, these constraints enforce the well known odd-denominator rule, which is seen to be a necessary property of all 1D patterns associated to quantum Hall states with minimum torus degeneracy. However, the same constraints also have implications for the non-Abelian states possible within this framework. In simple cases, including the ν = 1 Moore-Read state and the ν = 3/2 level 3 Read-Rezayi state, the filling factor and the torus degeneracy uniquely specify the possible patterns, and thus all physical properties that are encoded in them. It is also shown that some states, such as the "strong p-wave pairing state", cannot in principle be described through patterns.Introduction. The study of fractional quantum Hall (FQH) liquids has been among the most intriguing problems in condensed matter physics during the past few decades, in both theory and experiment. On the theoretical side, the construction of variational many-body wave functions has traditionally played a pivotal role[1]. In principle, the possible variational constructions are limitless. A systematic classification of FQH phases therefore requires additional constraints, such as simplicity in a composite fermion picture [2]. Another program to implement such constraints is to require that the trial wave functions can be obtained as conformal blocks in certain conformal field theories [3]. The problem is then relegated to identifying all conformal field theories leading to permissible wave functions. On the other hand, it has recently become appreciated that a large class of trial wave functions can be characterized by simple sequences of integers, either through the thin torus limit and adiabatic continuity [4][5][6][7][8][9], or through Jack polynomials [10]. The patterns of integers associated with viable quantum Hall states are in turn subject to a number of consistency requirements, such as rotational invariance of the associated Jack polynomials, or constraints on the associated "patterns of zeros" studied in Ref. 11. A complete set of consistency requirements is desirable in order to understand the possible quantum numbers of all quantum Hall phases that are accessible within this framework. In this paper, it will be shown that the one-dimensional (1D) patterns associated with the ground state sectors of a quantum Hall phase are highly constrained by modular invariance on the torus. In the simplest case, the implication of these constraints is the well-known "odddenominator-rule", which is found to be required within this framework for all quantum Hall states that have the "minimum torus degeneracy". Such states are necessarily Abelian, and include states in the Haldane-Halperin hierarchy. Furthermore, in some other cases of interest, it is found that the filling factor and the torus degeneracy already completely determine the associated se...

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Incompressible Quantum Liquids and New Conservation Laws

Cited by 139 publications

References 28 publications

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

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

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

S-Duality Constraints on 1D Patterns Associated with Fractional Quantum Hall States

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