Hall effect, edge states, and Haldane exclusion statistics in two-dimensional space

Ye, F.; Marchetti, P. A.; Su, Zhixun; Yu, Li

doi:10.1103/physrevb.92.235151

Cited by 10 publications

(24 citation statements)

References 45 publications

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“…This result can also be derived using our previous results on the mutual statistics in two-dimensional Hall insulator consisting of multiple species of anyons, where we proved the parameters g ab of mutual exclusion satisfy g ab = 2πσ h,a αq a q b for all flavors in the presence of Chern-Simons coupling(see the appendix of Ref. [23]). We now turn to the mutual statistics of one-dimensional chiral anyons.…”

Section: Mutual Statistics Of Multiple Species Of Chiral Anyonssupporting

confidence: 79%

“…As we proved in Ref. [23], the bulk anyon also obeys the mutual fractional exclusion statistics induced by braiding particles, and the particle density is shifted to a α-dependent value ρ B,a (α) for each flavor. The corresponding total flux density is then 2πα N f a=1 q a ρ B,a (α), therefore we obtain a relation between ρ 0 B,a and ρ B,a (α) as following…”

Section: Mutual Statistics Of Multiple Species Of Chiral Anyonssupporting

confidence: 62%

“…which indicates that the Haldane's statistical interaction g is ∓α. The relation between g and α for a Hall insulator with a general Hall conductance σ h has been given in a different way in our previous study [23]. Inspired by the bulk result, one may expect that the edge mode may also exhibit non-trivial fractional exclusion statistics.…”

Section: Fractional Statistics For a Chiral Anyon Systemmentioning

confidence: 96%

“…In the present study, we adopt the fermion-based Chern-Simons theory to unambiguously define the braid statistics. This is also the same framework adopted in our previous study on two dimensional fractional statistics [23], but to discuss braid statistics in one dimension we need a careful dimensional reduction following the technique developed in [33]. In this setup, we restrict to impenetrable two-body interactions, to have a well-defined braid statistics.…”

Section: Introductionmentioning

confidence: 99%

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Fractional exclusion and braid statistics in one dimension: a study via dimensional reduction of Chern–Simons theory

Marchetti

et al. 2017

J. Phys. A: Math. Theor.

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The relation between braid and exclusion statistics is examined in onedimensional systems, within the framework of Chern-Simons statistical transmutation in gauge invariant form with an appropriate dimensional reduction. If the matter action is anomalous, as for chiral fermions, a relation between braid and exclusion statistics can be established explicitly for both mutual and nonmutual cases. However, if it is not anomalous, the exclusion statistics of emergent low energy excitations is not necessarily connected to the braid statistics of the physical charged fields of the system. Finally, we also discuss the bosonization of one-dimensional anyonic systems through T-duality.PACS numbers: 05.30.Pr Fractional statistics systems (anyons, etc.) ‡ Dedicated to the memory of Mario Tonin.

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Section: Mutual Statistics Of Multiple Species Of Chiral Anyonssupporting

confidence: 79%

Section: Mutual Statistics Of Multiple Species Of Chiral Anyonssupporting

confidence: 62%

Section: Fractional Statistics For a Chiral Anyon Systemmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fractional exclusion and braid statistics in one dimension: a study via dimensional reduction of Chern–Simons theory

Marchetti

et al. 2017

J. Phys. A: Math. Theor.

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“…The ground state of Kitaev spin model [8] represents a typical quantum paramagnetism dubbed quantum spin liquid, in which the spin degree of freedom does not freeze even at zero temperature [11]. Quantum spin liquid displays various patterns of long-range quantum entanglement [8,12,13] and supports the fractional excitations [14][15][16][17][18][19][20]. Kitaev interactions have been identified in layered honeycomb magnetic materials, such as α-Li 2 IrO 3 [21] and α-RuCl 3 [22].…”

mentioning

confidence: 99%

Raman spectroscopy evidence for dimerization and Mott collapse in α−RuCl3 under pressures

Chen

Gan

et al. 2019

Phys. Rev. Materials

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We perform Raman spectroscopy studies on α-RuCl3 at room temperature to explore its phase transitions of magnetism and chemical bonding under pressures. The Raman measurements resolve two critical pressures, about p1 = 1.1 GPa and p2 = 1.7 GPa, involving very different intertwining behaviors between the structural and magnetic excitations. With increasing pressures, a stacking order phase transition of α-RuCl3 layers develops at p1 = 1.1 GPa, indicated by the new Raman phonon modes and the modest Raman magnetic susceptibility adjustment. The abnormal softening and splitting of the Ru in-plane Raman mode provide direct evidence of the in-plane dimerization of the Ru-Ru bonds at p2 = 1.7 GPa. The Raman susceptibility is greatly enhanced with pressure increasing and sharply suppressed after the dimerization. We propose that the system undergoes Mott collapse at p2 = 1.7 GPa and turns into a dimerized correlated band insulator. Our studies demonstrate competitions between Kitaev physics, magnetism, and chemical bondings in Kitaev compounds.arXiv:1807.08211v1 [cond-mat.str-el]

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Universality in Cuprates: A Gauge Approach

Marchetti¹,

Bighin²

2016

J Low Temp Phys

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In high-Tc cuprates,many quantities exhibit a non-Fermi liquid universality\ud hinting at a very peculiar structure of the underlying pairing mechanism for superconductivity:\ud in this work, we focus on the universality for the in-plane resistivity and the\ud superfluid density. We outline the previously developed spin–charge gauge approach\ud to superconductivity in hole-doped cuprates: we decompose the hole of the t −t' − J\ud model for the CuO2 planes as the product of a spinful, chargeless gapped spinon and\ud a spinless, charged holon with Fermi surface. Each one of these particle excitations is\ud bound to a statistical gauge flux, allowing one to optimize their statistics.We show that\ud this model allows for a natural interpretation of the universality: within this approach,\ud under suitable conditions, the spinonic and holonic contributions to a response function\ud sum up according to the Ioffe–Larkin rule.We argue that, if the spinonic contribution\ud dominates, then one should expect strongly non-Fermi-liquid-like universality, due\ud to the insensitivity of spinons to Fermi surface details. The in-plane resistivity and\ud superfluid density are indeed dominated by spinons in the underdoped region.We theoretically\ud derive these quantities, discussing their universal behaviours and comparing\ud them with experimental data

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Hall effect, edge states, and Haldane exclusion statistics in two-dimensional space

Cited by 10 publications

References 45 publications

Fractional exclusion and braid statistics in one dimension: a study via dimensional reduction of Chern–Simons theory

Fractional exclusion and braid statistics in one dimension: a study via dimensional reduction of Chern–Simons theory

Raman spectroscopy evidence for dimerization and Mott collapse in α−RuCl3 under pressures

Universality in Cuprates: A Gauge Approach

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