Fractional statistics in anyon collisions

Bartolomei, Hugo; Kumar, Manohar; Bisognin, R.; Marguerite, Arthur; Berroir, Jean-Marc; Bocquillon, Erwann; Plaçais, Bernard; Cavanna, A.; Dong, Qing; Gennser, U.; Jin, Yong; Fève, Gwendal

doi:10.1126/science.aaz5601

Cited by 321 publications

(231 citation statements)

References 42 publications

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“…The obtained narrow width (a few nanoseconds) of the fractionalized wave packets encourages studying microscopic fractionalization processes including neutral modes and heat generation, which can be used to identify the appropriate effective model [34][35][36]49 . The deterministic fractionalization processes may benefit the search for non-trivial anyonic statistics of fractional charges 48,[50][51][52][53] .…”

Section: Discussionmentioning

confidence: 99%

Quantized charge fractionalization at quantum Hall Y junctions in the disorder dominated regime

et al. 2021

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Fractionalization is a phenomenon where an elementary excitation partitions into several pieces. This picture explains non-trivial transport through a junction of one-dimensional edge channels defined by topologically distinct quantum Hall states, for example, a hole-conjugate state at Landau-level filling factor ν = 2/3. Here we employ a time-resolved scheme to identify an elementary fractionalization process; injection of charge q from a non-interaction region into an interacting and scattering region of one-dimensional channels results in the formation of a collective excitation with charge (1−r)q by reflecting fractionalized charge rq. The fractionalization factors, r = 0.34 ± 0.03 for ν = 2/3 and r = 0.49 ± 0.03 for ν = 2, are consistent with the quantized values of 1/3 and 1/2, respectively, which are expected in the disorder dominated regime. The scheme can be used for generating and transporting fractionalized charges with a well-defined time course along a well-defined path.

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Section: Discussionmentioning

confidence: 99%

Quantized charge fractionalization at quantum Hall Y junctions in the disorder dominated regime

et al. 2021

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“…The topological spins determine the exchange statistics of anyons, predicted to appear in interferometry experiments [49], though experimental observation remains elusive [65]. A measurement of anyonic statistics via current correlations [66] was recently reported in the Laughlin 1/3 quantum Hall state [67].…”

Section: Phase Of Mattermentioning

confidence: 99%

Intrinsic sign problem in fermionic and bosonic chiral topological matter

Golan

Smith

Ringel

2020

Phys. Rev. Research

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The infamous sign problem leads to an exponential complexity in Monte Carlo simulations of generic many-body quantum systems. Nevertheless, many phases of matter are known to admit a sign-problem-free representative, allowing efficient simulations on classical computers. Motivated by long-standing open problems in many-body physics, as well as fundamental questions in quantum complexity, the possibility of intrinsic sign problems, where a phase of matter admits no sign-problem-free representative, was recently raised but remains largely unexplored. Here we establish the existence of an intrinsic sign problem in a broad class of gapped, chiral, topological phases of matter. Within this class, we exclude the possibility of stoquastic Hamiltonians for bosons (or "qudits") and of sign-problem-free determinantal Monte Carlo algorithms for fermions. The intrinsically sign-problematic class of phases we identify is defined in terms of topological invariants with clear observable signatures: the chiral central charge and the topological spins of anyons. We obtain analogous results for phases that are spontaneously chiral, and present evidence for an extension of our results that applies to both chiral and nonchiral topological matter.

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“…As our ability to design and control materials exhibiting these phases relies heavily on simulations, it is desirable to understand which TQFTs have intrinsic sign problems. This is especially relevant in light of the recent experimental demonstration of fractional anyon statistics [30]. However, apart from Hastings' work [14], it remains unclear whether TQFTs more generally lead to intrinsic sign problems and whether this can be diagnosed based on the TQFT data: the T and S matrices defining the exchange and mutual statistics of the anyonic quasiparticles in the theory.…”

Section: Introductionmentioning

confidence: 99%

Intrinsic sign problems in topological quantum field theories

Smith

Golan

Ringel

2020

Phys. Rev. Research

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The sign problem is a widespread numerical hurdle preventing us from simulating the equilibrium behavior of various problems at the forefront of physics. Focusing on an important subclass of such problems, bosonic (2 + 1)-dimensional topological quantum field theories, here we provide a simple criterion to diagnose intrinsic sign problems-that is, sign problems that are inherent to that phase of matter and cannot be removed by any local unitary transformation. Explicitly, if the exchange statistics of the anyonic excitations do not form complete sets of roots of unity, then the model has an intrinsic sign problem. This establishes a concrete connection between the statistics of anyons, contained in the modular S and T matrices, and the presence of a sign problem in a microscopic Hamiltonian. Furthermore, it places constraints on the phases that can be realized by stoquastic Hamiltonians. We prove this and a more restrictive criterion for the large set of gapped bosonic models described by an Abelian topological quantum field theory at low-energy, and we offer evidence that it applies more generally with analogous results for non-Abelian and chiral theories.

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Fractional statistics in anyon collisions

Cited by 321 publications

References 42 publications

Quantized charge fractionalization at quantum Hall Y junctions in the disorder dominated regime

Quantized charge fractionalization at quantum Hall Y junctions in the disorder dominated regime

Intrinsic sign problem in fermionic and bosonic chiral topological matter

Intrinsic sign problems in topological quantum field theories

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