Gaffnian holonomy through the coherent state method

Flavin, John; Thomale, Ronny; Seidel, Alexander

doi:10.1103/physrevb.86.125316

Cited by 12 publications

(40 citation statements)

References 72 publications

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“…It has certainly some desirable properties like good overlap with the true ground state for Coulomb interactions. Several studies have been devoted to its properties [12][13][14][15][16][17][18][19]. However, there is a potential problem which has been raised originally by Read [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Absence of a gap in the Gaffnian state

Jolicœur¹,

Mizusaki²,

Lecheminant³

2014

Phys. Rev. B

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We study the Gaffnian trial wave function proposed to describe fractional quantum Hall correlations at Bose filling factor ν = 2/3 and Fermi filling ν = 2/5. A family of Hamiltonians interpolating between a hard-core interaction for which the physics is known and a projector whose ground state is the Gaffnian is studied in detail. We give evidence for the absence of a gap by using large-scale exact diagonalizations in the spherical geometry. This is in agreement with recent arguments based on the fact that this wave function is constructed from a nonunitary conformal field theory. By using the cylinder geometry, we discuss in detail the nature of the underlying minimal model and we show the appearance of heterotic conformal towers in the edge energy spectrum where left and right movers are generated by distinct primary operators.

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Section: Introductionmentioning

confidence: 99%

Absence of a gap in the Gaffnian state

Jolicœur¹,

Mizusaki²,

Lecheminant³

2014

Phys. Rev. B

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“…(Note that a similar but different analysis can also be executed on the sphere by analyzing the root partitions of the parent Hamiltonian null space [55]). The detailed procedure for finding the root patterns of Halperin bilayer states was given in Ref.…”

Section: Fermionic Gaffnianmentioning

confidence: 99%

Geometric Construction of Quantum Hall Clustering Hamiltonians

2015

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Many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain "pseudopotential" Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi Z 3 states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated many-body interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent SUðnÞ cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.

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“…Recently, multi-LL wavefunctions have been discussed on the torus [45]. If the dominance patterns established here are understood as "thin torus (TT) patterns", there exists a well-defined "coherent state" method to associate braiding statistics to the excitations of the underlying state [46][47][48][49][50][51]. In this regard, we first observe that if we discard the subscripts σ R,L and s z in the dominance patterns satisfying the EPP, the resulting reduced patterns of 1s and 0s satisfy the GPP associated with TT/dominance patterns of the ν=1/2 Moore-Read (MR) Pfaffian state: There are no more than two 1s in any four adjacent sites.…”

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confidence: 99%

Entangled Pauli principles: The DNA of quantum Hall fluids

et al. 2018

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A formalism is developed for the rigorous study of solvable fractional quantum Hall parent Hamiltonians with Landau level mixing. The idea of organization through "generalized Pauli principles" is expanded to allow for root level entanglement, giving rise to "entangled Pauli principles". Through the latter, aspects of the effective field theory description become ingrained in exact microscopic solutions for a great wealth of phases for which no similar single Landau level description is known. We discuss in detail braiding statistic, edge theory, and rigorous zero-mode counting for the Jain-221 state as derived from a microscopic Hamiltonian. The relevant root-level entanglement is found to feature an AKLT-type MPS structure associated with an emergent SU(2)-symmetry.

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Gaffnian holonomy through the coherent state method

Cited by 12 publications

References 72 publications

Absence of a gap in the Gaffnian state

Absence of a gap in the Gaffnian state

Geometric Construction of Quantum Hall Clustering Hamiltonians

Entangled Pauli principles: The DNA of quantum Hall fluids

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