Model states for a class of chiral topological order interfaces

Crépel, Valentin; Claussen, N.; Estienne, Benoît; Regnault, Nicolas

doi:10.1038/s41467-019-09168-z

Cited by 34 publications

(55 citation statements)

References 54 publications

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“…Indeed, entanglement entropy is a well-established probe of quantum matter and of gapless edge modes in particular, as was shown e.g. in 2D droplets [39,51], at interfaces between fractional quantum Hall states [52][53][54], or in 3D topological insulators with hinge modes [55,56]. Since we are dealing here with non-interacting fermions, calculations simplify considerably [40][41][42][43][44]: one can relate the entanglement spectrum to that of a subregion-restricted correlation matrix, reducing the computation of many-body entanglement to a one-body problem.…”

Section: Quantum Entanglementmentioning

confidence: 90%

Ergodic edge modes in the 4D quantum Hall effect

2021

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The gapless modes on the edge of four-dimensional (4D) quantum Hall droplets are known to be anisotropic: they only propagate in one direction, foliating the 3D boundary into independent 1D conduction channels. This foliation is extremely sensitive to the confining potential and generically yields chaotic flows. Here we study the quantum correlations and entanglement of such edge modes in 4D droplets confined by harmonic traps, whose boundary is a squashed three-sphere. Commensurable trapping frequencies lead to periodic trajectories of electronic guiding centers; the corresponding edge modes propagate independently along S^1S1 fibers, forming a bundle of 1D conformal field theories over a 2D base space. By contrast, incommensurable frequencies produce quasi-periodic, ergodic trajectories, each of which covers its invariant torus densely; the corresponding correlation function of edge modes has fractal features. This wealth of behaviors highlights the sharp differences between 4D Hall droplets and their 2D peers; it also exhibits the dependence of 4D edge modes on the choice of trap, suggesting the existence of observable bifurcations due to droplet deformations.

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Section: Quantum Entanglementmentioning

confidence: 90%

Ergodic edge modes in the 4D quantum Hall effect

2021

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“…We have also put the bosonic model (m = 2) discussed in Ref. [29] under scrutiny of finite size ED. The results that we have obtained underline the microscopic validity of the model state and its applicability to both fermions and bosons.…”

Section: Data Availabilitymentioning

confidence: 99%

“…While powerful, these effective field theory approaches suffer from a complete lack of connection with a more physical, microscopic description. In order to overcome this limitation we have recently proposed a family of Matrix Product State (MPS) model wavefunctions for the Laughlin-Halperin interface capable of describing the whole system including both bulks and the interface [29]. We found that these MPSs faithfully describe the bulks intrinsic topological order while presenting the expected universal low-energy physics at the interface.…”

Section: Introductionmentioning

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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“…in Camino et al's interferometric experiments which aimed at demonstrating the fractional statistics [21]. There are also some proposals for creating interfaces with a non-Abelian state on at least one side [11,22,23].…”

Section: Introductionmentioning

confidence: 99%

Model wave functions for interfaces between lattice Laughlin states

Jaworowski

Nielsen

2020

Phys. Rev. B

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We use conformal field theory to construct model wavefunctions for an interface between lattice versions of a bosonic ν = 1/2 Laughlin state and a fermionic ν = 5/2 Moore-Read state. The properties of the resulting model state, such as particle density, correlation function and Rényi entanglement entropy are then studied using the Monte Carlo approach. Moreover, we construct the wavefunctions also for localized anyonic excitations (quasiparticles and quasiholes). We study their density profile, charge and statistics. We show that, similarly to the Laughlin-Laughlin case studied earlier, some anyons (the Laughlin Abelian ones) can cross the interface, while others (the non-Abelian ones) lose their anyonic character in such a process. Also, we argue that, under an assumption of local particle exchange, multiple interfaces give rise to a topological degeneracy, which can be interpreted as originating from Majorana zero modes.

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Model states for a class of chiral topological order interfaces

Cited by 34 publications

References 54 publications

Ergodic edge modes in the 4D quantum Hall effect

Ergodic edge modes in the 4D quantum Hall effect

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

Model wave functions for interfaces between lattice Laughlin states

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