Universal signatures of Dirac fermions in entanglement and charge fluctuations

Crépel, Valentin; Hackenbroich, Anna; Regnault, Nicolas; Estienne, Benoît

doi:10.1103/physrevb.103.235108

Cited by 10 publications

(11 citation statements)

References 77 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: 91%

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: 91%

Ergodic edge modes in the 4D quantum Hall effect

2021

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“…They are rather quasi-periodic, since Z n (α + 2π) = e 2πiδ(Φ) Z n (α) as anticipated below (6). Also note that (25) enjoys the relation Z (25) for Z1(α) with Φ = 0 for perimeters L = 2, 4, 10, and its (dashed) integral approximation (26). Both log Z1(α) and its approximation are divided by L for readability.…”

Section: Exact Charged Momentsmentioning

confidence: 95%

“…Both log Z1(α) and its approximation are divided by L for readability. The approximation becomes more accurate as L grows, save for the divergence at α = ±π (corresponding to Z1(±π) = 0 when Φ = 0) that cannot be captured by the integral (26). Around its maximum at α = 0, log Z1(α) behaves as a concave parabola, eventually giving the near-Gaussian behavior (27).…”

Section: Exact Charged Momentsmentioning

confidence: 99%

“…It captures e.g. the Luttinger parameter of 1D systems [14,24,25], detects and counts massless Dirac fermions in 2D [26], and measures the long-wavelength limit of the structure factor of gapped 2D liquids [27]. It was recently realized that internal symmetries also provide a natural decomposition of entanglement measures in sectors with definite values of the corresponding charge [28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

“…It was recently realized that internal symmetries also provide a natural decomposition of entanglement measures in sectors with definite values of the corresponding charge [28][29][30][31]. Such symmetry-resolved EEs and their relation to charge fluctuations have been studied in a number of contexts: criti-cal [30,[32][33][34][35][36][37][38][39][40][41] or gapped [42,43] 1D systems, topological phases [44][45][46], systems of free particles [26,[47][48][49][50][51][52][53][54][55][56], integrable models [57][58][59], and even gravity [60,61]. As it turns out, entropy typically spreads evenly among different symmetry sectors-a property dubbed equipartition of EE [32].…”

Section: Introductionmentioning

confidence: 99%

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Equipartition of Entanglement in Quantum Hall States

Oblak,

Regnault,

Estienne

2021

Preprint

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We study the full counting statistics (FCS) and symmetry-resolved entanglement entropies of integer and fractional quantum Hall states. For the filled lowest Landau level of spin-polarized electrons on an infinite cylinder, we compute exactly the charged moments associated with a cut orthogonal to the cylinder's axis. This yields the behavior of FCS and entropies in the limit of large perimeters: in a suitable range of fluctuations, FCS is Gaussian and entanglement spreads evenly among different charge sectors. Subleading charge-dependent corrections to equipartition are also derived. We then extend the analysis to Laughlin wavefunctions, where entanglement spectroscopy is carried out assuming the Li-Haldane conjecture. The results confirm equipartition up to small charge-dependent terms, and are then matched with numerical computations based on exact matrix product states.

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Holographic entanglement renormalisation for fermionic quantum matter

Mukherjee,

Patra,

Lal

2024

J. Phys. A: Math. Theor.

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We demonstrate the emergence of a holographic dimension in a system of 2D non-interacting Dirac fermions placed on a torus, by studying the scaling of multipartite entanglement measures under a sequence of renormalisation group (RG) transformations applied in momentum space. Geometric measures defined in this emergent space can be related to the RG beta function of the spectral gap, hence establishing a holographic connection between the spatial geometry of the emergent spatial dimension and the entanglement properties of the boundary quantum theory. We prove, analytically, that changing the boundedness of the holographic space involves a topological transition accompanied by a critical Fermi surface in the boundary theory. We go on to show that this results in the formation of a quantum wormhole geometry that connects the UV and the IR of the emergent dimension. The additional conformal symmetry at the transition also supports a relation between the emergent metric and the stress-energy tensor. In the presence of an Aharonov–Bohm flux, the entanglement gains a geometry-independent piece which is shown to be topological, sensitive to changes in boundary conditions, and related to the Luttinger volume of the system. Upon the insertion of a strong transverse magnetic field, we show that the Luttinger volume is linked to the Chern number of the occupied single-particle Landau levels.

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Universal signatures of Dirac fermions in entanglement and charge fluctuations

Cited by 10 publications

References 77 publications

Ergodic edge modes in the 4D quantum Hall effect

Ergodic edge modes in the 4D quantum Hall effect

Equipartition of Entanglement in Quantum Hall States

Holographic entanglement renormalisation for fermionic quantum matter

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