Fractionalization and Dynamics of Anyons and Their Experimental Signatures in the 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">/</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math>
 Fractional Quantum Hall State

Trung, Ha Quang; Yang, Bo

doi:10.1103/physrevlett.127.046402

Cited by 11 publications

(9 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, and in particular, the quasihole excitations can be fractionalized and carry the charge of e/10. This is analogous to the nematic FQH phase at ν = 1/3 observed in the experiments and the fractionalization of the Laughlin-1/3 quasiholes near the phase transition [140]. It would thus be exciting if the hollow-core modes, characterized by fractionalized Laughlin-1/5 quasiholes, could be observed in experiments.…”

Section: Experimental Significancesupporting

confidence: 64%

“…Thus this quantity became an important index to distinguish the nature of non-Abelian states because Hall conductance experiments are incapable of detecting the signature of neutral non-Abelions, and was afterward found to be relevant to the central charge of the CFT describing the FQH phase as well [137]. Furthermore, they also studied the analogous FQH state of a d-wave paired state of spinless bosons in detail, which is now called the Haffnian state [138][139][140].…”

Section: Harvest Time: 1993 -2003mentioning

confidence: 99%

“…We have introduced the microscopic theory about the collective neutral excitations with spin-2 in FQH phases, called the graviton modes as a typical manifestation of the interplay between topology and geometry. While Lorentz invariance is absent in this (2 + 1)-dimensional space-time, these 2D graviton modes encode topological information about their respective FQH phases, and their dynamics lead to rich physics ranging from ground state incompressibility to the dynamical phase transitions of the low-lying excitations [140,354]. The effective field theory studying the graviton modes has been proposed by using the Newton-Carton metric, and various experimental proposals for the observation of these modes have been put forward [187,236,238,318,321,322,[324][325][326]355].…”

Section: Microscopic Theory Of Multiple Graviton Modesmentioning

confidence: 99%

See 2 more Smart Citations

Graviton modes in fractional quantum hall liquids

Wang¹

View full text Add to dashboard Cite

The fractional quantum Hall fluid is a two-dimensional quantum fluid of electrons subject to a strong magnetic field at low temperatures. Neutral excitations in a fractional quantum Hall droplet define the incompressibility gap of the topological phase. Among these states, there are some specific modes in the long-wavelength limit that can be understood as "spin-2 gravitons". In this thesis, we will introduce a set of analytical results for the energy gap of the graviton modes for model Hamiltonians in the thermodynamic limit, which is governed by a well-defined and universal characteristic tensor. These results can help to construct model Hamiltonians for the graviton modes of different FQH phases and elucidate a hierarchical structure of conformal Hilbert spaces (null spaces of model Hamiltonians) containing the graviton modes and their corresponding ground states. An isomorphism can be defined for these conformal Hilbert spaces, and the mapping between them can be regarded as a more rigorous and general reinterpretation of the composite fermionization of FQH states, with naturally emergent composite fermions (each consisting of one electron and an even number of fluxes). The results from exact diagonalization will be shown, which confirm that for gapped phases, low-lying neutral excitations can undergo a phase transition even when the ground state remains in the same phase. Furthermore, the gaplessness of the Gaffnian state could be testified based on this formalism with further numerical experiments. Recently there has been numerical evidence implying the signature of multiple graviton modes. We will introduce the microscopic theory for the emergence of multiple gravitons in fractional quantum Hall droplets based on composite fermionization and the well-defined particle-hole conjugate within a specific conformal Hilbert space. This reveals the dynamical nature of this phenomenon and provides theoretical insights into the chirality and the "merging and splitting" behaviors of the graviton modes. The experimental relevance of multiple graviton modes will be discussed. The microscopic theory of gravitons can also provide valuable insights into the field-theoretical approaches.

show abstract

Section: Experimental Significancesupporting

confidence: 64%

Section: Harvest Time: 1993 -2003mentioning

confidence: 99%

Section: Microscopic Theory Of Multiple Graviton Modesmentioning

confidence: 99%

See 1 more Smart Citation

Graviton modes in fractional quantum hall liquids

Wang¹

View full text Add to dashboard Cite

show abstract

“…In chapter 3, we give the definition of conformal Hilbert spaces (CHS) in terms of angular momentum eigenstate counting, and describe how this counting establishes the one-to-one mapping between different CHS. Chapter 4 details a specific case where the CHS reveals relation between the Laughlin and the Gaffnian and how this picture helps us understand the physics of nematic quantum Hall phase [85]. The entirety of chapter 5 is spent discussing the microscopic description of the spin-statistics relation of anyons in FQH systems [86].…”

Section: Organization Of the Thesismentioning

confidence: 99%

“…2.5). This is the idea behind the LEC formalism: an LEC condition is a classical constraint given by a triplet of number {n 1 , m formalism can reproduce all of the known FQH Jacks, while being able to produce more FQH states that are not Jacks, such as the Haffnian state [52,60,85,113].…”

Section: Local Exclusion Constraint Formalismmentioning

confidence: 99%

Dynamical and statistical properties of anyons in fractional quantum hall effect

View full text Add to dashboard Cite

The quantum Hall effect has been the prototypical example for many emerging fields of Physics, including the study of topological phases of matter, topological order, and topological insulators. The objects of interest in this thesis are anyons, which are elementary excitations in fractional quantum Hall (FQH) fluids. Anyons are quasiparticles with fractional charge and fractional statistics. The latter property makes it a subject of immense interest due to application in fault-tolerant quantum computing. Here, we employ a perspective that anyons are the appropriate degree of freedom to describe the relevant physics of FQH systems. This is because when a topological phase is assumed and the energy gap goes to infinity, anyons ("quasiholes") are the only possible elementary excitations, since they are not energetically punished by the correspondng model Hamiltonian. With respect to a realistic Hamiltonian, however, this choice of degree of freedom depends on the exact effective interaction in the system. For example, while the Laughlin state is the model state at filling factor n + 1/3 (where n is some integer), when the effective electron-electron interaction is more long-ranged, the quasiholes of a Gaffnian state may be excited and become the better degree of freedom to describe physics in the same filling factor. This perspective results in a surprising observation that a Laughlin quasihole may fractionalize under certain conditions, leading to a quasiparticle of charge e/6 that can potentially be detected in experiments.Another important aspect of anyons is their intrinsic spin and the corresponding spin-statistics relation, which must account for the fact that FQH anyons are not point particles, but objects with finite sizes and intricate internal structures. Our investigation leads to a rigorous derivation of the general spin-statistics relation for anyons in Abelian FQH phases. Furthermore, we show it is possible to fully capture the important features of the statistics by a conformal Hilbert space (CHS) description. Our analysis provides the necessary tools to study such geometric effects, which we use to investigate how disorder in a realistic system may affect different experimental schemes for measuring anyon statistics.

show abstract

Geometric fluctuation of conformal Hilbert spaces and multiple graviton modes in fractional quantum Hall effect

Wang

Yang

2023

Nat Commun

Self Cite

View full text Add to dashboard Cite

Neutral excitations in fractional quantum Hall (FQH) fluids define the incompressibility of topological phases, a species of which can show graviton-like behaviors and are thus called the graviton modes (GMs). Here, we develop the microscopic theory for multiple GMs in FQH fluids and show explicitly that they are associated with the geometric fluctuation of well-defined conformal Hilbert spaces (CHSs), which are hierarchical subspaces within a single Landau level, each with emergent conformal symmetry and continuously parameterized by a unimodular metric. This leads to several statements about the number and the merging/splitting of GMs, which are verified numerically with both model and realistic interactions. We also discuss how the microscopic theory can serve as the basis for the additional Haldane modes in the effective field theory description and their experimental relevance to realistic electron-electron interactions.

show abstract

Fractionalization and Dynamics of Anyons and Their Experimental Signatures in the ν=n+1/3 Fractional Quantum Hall State

Cited by 11 publications

References 52 publications

Graviton modes in fractional quantum hall liquids

Graviton modes in fractional quantum hall liquids

Dynamical and statistical properties of anyons in fractional quantum hall effect

Geometric fluctuation of conformal Hilbert spaces and multiple graviton modes in fractional quantum Hall effect

Contact Info

Product

Resources

About