Geometric Construction of Quantum Hall Clustering Hamiltonians

Lee, Ching Hua; Papić, Zlatko; Thomale, Ronny

doi:10.1103/physrevx.5.041003

Cited by 43 publications

(42 citation statements)

References 71 publications

(181 reference statements)

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“…µ ↑ = ∞) [26]. Indeed, H int reduces to the zero-th and first Haldane pseudopotentials [27,44]. We now choose µ ↑ (r) such that the quadratic part reads…”

Section: Resultsmentioning

confidence: 99%

Microscopic study of the Halperin–Laughlin interface through matrix product states

et al. 2019

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Interfaces between topologically distinct phases of matter reveal a remarkably rich phenomenology. We study the experimentally relevant interface between a Laughlin phase at filling factor ν = 1/3 and a Halperin 332 phase at filling factor ν = 2/5. Based on our recent construction of chiral topological interfaces ( Nat. Commun . 10.1038/s41467-019-09168-z; 2019), we study a family of model wavefunctions that captures both the bulk and interface properties. These model wavefunctions are built within the matrix product state framework. The validity of our approach is substantiated through extensive comparisons with exact diagonalization studies. We probe previously unreachable features of the low energy physics of the transition. We provide, amongst other things, the characterization of the interface gapless mode and the identification of the spin and charge excitations in the many-body spectrum. The methods and tools presented are applicable to a broad range of topological interfaces.

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“…µ ↑ = ∞) [26]. Indeed, H int reduces to the zero-th and first Haldane pseudopotentials [27,44]. We now choose µ ↑ (r) such that the quadratic part reads…”

Section: Resultsmentioning

confidence: 99%

Microscopic study of the Halperin–Laughlin interface through matrix product states

et al. 2019

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“…Indeed, only recently the second quantized presentation of FQH Hamiltonians has become a subject of interest in its own right. 27,36,37,59 For one thing, it can be argued that this approach more readily gives access to spectral properties at finite energies. 60 For another, the second quantized approach seems to be effective also in unravelling the zero mode structure of special Hamiltonians, as the present example demonstrates.…”

Section: Discussionmentioning

confidence: 99%

Jain-2/5 parent Hamiltonian: Structure of zero modes, dominance patterns, and zero mode generators

2017

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We analyze general zero mode properties of the parent Hamiltonian of the unprojected Jain-2/5 state. We characterize the zero mode condition associated to this Hamiltonian via projection onto a four-dimensional two-particle subspace for given pair angular momentum, for the disk and similarly for the spherical geometry. Earlier numerical claims in the literature about ground state uniqueness on the sphere are substantiated on analytic grounds, and related results are derived. Preference is given to second quantized methods, where zero mode properties are derived not from given analytic wave functions, but from a "lattice" Hamiltonian and associated zero mode conditions. This method reveals new insights into the guiding-center structure of the unprojected Jain-2/5 state, in particular a system of dominance patterns following a "generalized Pauli principle", which establishes a complete one-to-one correspondence with the edge mode counting. We also identify one-body operators that function as generators of zero modes.

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“…Using the 3-body parent Hamiltonian [110,111] for the model wavefunction in Eq. (13), we have verified this is indeed the case on the torus.…”

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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Geometric Construction of Quantum Hall Clustering Hamiltonians

Cited by 43 publications

References 71 publications

Microscopic study of the Halperin–Laughlin interface through matrix product states

Microscopic study of the Halperin–Laughlin interface through matrix product states

Jain-2/5 parent Hamiltonian: Structure of zero modes, dominance patterns, and zero mode generators

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

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