skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Statistics of Fractionalized Excitations through Threshold Spectroscopy

Abstract

We show that neutral anyonic excitations have a signature in spectroscopic measurements of materials: The low-energy onset of spectral functions near the threshold follows universal power laws with an exponent that depends only on the statistics of the anyons. This provides a route, using experimental techniques such as neutron scattering and tunneling spectroscopy, for detecting anyonic statistics in topologically ordered states such as gapped quantum spin liquids and hypothesized fractional Chern insulators. Our calculations also explain some recent theoretical results in spin systems.

Authors:
 [1];  [2];  [3];  [4]
  1. Max-Planck-Inst. für Physik komplexer Systeme, Dresden (Germany)
  2. Technion-Israel Inst. of Tech., Haifa (Israel); Johns Hopkins Univ., Baltimore, MD (United States)
  3. Max-Planck-Inst. für Physik komplexer Systeme, Dresden (Germany); Technische Univ. Munchen, Garching (Germany)
  4. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Stockholm Univ. (Sweden); Arizona State Univ., Tempe, AZ (United States); Shanghai Jiao Tong Univ. (China)
Publication Date:
Research Org.:
Johns Hopkins Univ., Baltimore, MD (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1505576
Alternate Identifier(s):
OSTI ID: 1361005
Grant/Contract Number:  
FG02-08ER46544; SC0012567; FG02-08-ER46544
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 118; Journal Issue: 22; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Morampudi, Siddhardh C., Turner, Ari M., Pollmann, Frank, and Wilczek, Frank. Statistics of Fractionalized Excitations through Threshold Spectroscopy. United States: N. p., 2017. Web. doi:10.1103/physrevlett.118.227201.
Morampudi, Siddhardh C., Turner, Ari M., Pollmann, Frank, & Wilczek, Frank. Statistics of Fractionalized Excitations through Threshold Spectroscopy. United States. doi:10.1103/physrevlett.118.227201.
Morampudi, Siddhardh C., Turner, Ari M., Pollmann, Frank, and Wilczek, Frank. Wed . "Statistics of Fractionalized Excitations through Threshold Spectroscopy". United States. doi:10.1103/physrevlett.118.227201. https://www.osti.gov/servlets/purl/1505576.
@article{osti_1505576,
title = {Statistics of Fractionalized Excitations through Threshold Spectroscopy},
author = {Morampudi, Siddhardh C. and Turner, Ari M. and Pollmann, Frank and Wilczek, Frank},
abstractNote = {We show that neutral anyonic excitations have a signature in spectroscopic measurements of materials: The low-energy onset of spectral functions near the threshold follows universal power laws with an exponent that depends only on the statistics of the anyons. This provides a route, using experimental techniques such as neutron scattering and tunneling spectroscopy, for detecting anyonic statistics in topologically ordered states such as gapped quantum spin liquids and hypothesized fractional Chern insulators. Our calculations also explain some recent theoretical results in spin systems.},
doi = {10.1103/physrevlett.118.227201},
journal = {Physical Review Letters},
number = 22,
volume = 118,
place = {United States},
year = {2017},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Figures / Tables:

FIG. 1 FIG. 1: (a) In phases with topological order, scattering processes can create fractionalized anyonic excitations above some threshold energy. (b) The statistics of the excitations mediate long-range effects between them.

Save / Share:

Works referenced in this record:

Classifying fractionalization: Symmetry classification of gapped Z 2 spin liquids in two dimensions
journal, March 2013


Statistics of Quasiparticles and the Hierarchy of Fractional Quantized Hall States
journal, April 1984


Quantum orders and symmetric spin liquids
journal, April 2002


Numerical study of a transition between Z 2 topologically ordered phases
journal, July 2014

  • Morampudi, Siddhardh C.; von Keyserlingk, Curt; Pollmann, Frank
  • Physical Review B, Vol. 90, Issue 3
  • DOI: 10.1103/PhysRevB.90.035117

Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model
journal, February 2001


Equivalence of the resonating-valence-bond and fractional quantum Hall states
journal, November 1987


On the Behavior of Cross Sections Near Thresholds
journal, May 1948


Topological Characterization of Fractional Quantum Hall Ground States from Microscopic Hamiltonians
journal, June 2013


Magnetic Flux, Angular Momentum, and Statistics
journal, April 1982


Thermopower as a possible probe of non-Abelian quasiparticle statistics in fractional quantum Hall liquids
journal, March 2009


The nature of the three-anyon wave functions
journal, April 1995


Detecting Chiral Edge States in the Hofstadter Optical Lattice
journal, June 2012


Quantum spin liquids in the absence of spin-rotation symmetry: Application to herbertsmithite
journal, December 2013


Detecting Topological Order in a Ground State Wave Function
journal, March 2006


Topological Entanglement Entropy
journal, March 2006


Dynamics and Transport of the Z 2 Spin Liquid: Application to κ ( ET ) 2 Cu 2 ( CN ) 3
journal, April 2009


Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
journal, August 2005


Quantum Mechanics of Fractional-Spin Particles
journal, October 1982


Interferometry of non-Abelian anyons
journal, November 2008

  • Bonderson, Parsa; Shtengel, Kirill; Slingerland, J. K.
  • Annals of Physics, Vol. 323, Issue 11
  • DOI: 10.1016/j.aop.2008.01.012

Observable Bulk Signatures of Non-Abelian Quantum Hall States
journal, April 2009


Statistical mechanics of anyons
journal, January 1985


Flux quantization for semions on a torus
journal, November 1993


Quasiparticle statistics and braiding from ground-state entanglement
journal, June 2012


Anyons on a torus
journal, October 1990


Measurement of filling factor 5/2 quasiparticle interference with observation of charge e/4 and e/2 period oscillations
journal, May 2009

  • Willett, R. L.; Pfeiffer, L. N.; West, K. W.
  • Proceedings of the National Academy of Sciences, Vol. 106, Issue 22
  • DOI: 10.1073/pnas.0812599106

The Resonating Valence Bond State in La2CuO4 and Superconductivity
journal, March 1987


Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States
journal, July 2015


Adiabatic Cooling with Non-Abelian Anyons
journal, August 2010


Fractional statistics on a torus
journal, April 1990


Topology of the resonating valence-bond state: Solitons and high- T c superconductivity
journal, June 1987

  • Kivelson, Steven A.; Rokhsar, Daniel S.; Sethna, James P.
  • Physical Review B, Vol. 35, Issue 16
  • DOI: 10.1103/PhysRevB.35.8865

Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
journal, October 2010


Statistics of the excitations of the resonating-valence-bond state
journal, October 1989


Fractional Quantum Hall States at Zero Magnetic Field
journal, June 2011


Two-Dimensional Magnetotransport in the Extreme Quantum Limit
journal, May 1982


High-Temperature Fractional Quantum Hall States
journal, June 2011


Spin liquids in frustrated magnets
journal, March 2010


Detecting Non-Abelian Anyons by Charging Spectroscopy
journal, March 2013


Chiral spin states and superconductivity
journal, June 1989


Topological excitations and the dynamic structure factor of spin liquids on the kagome lattice
journal, March 2014

  • Punk, Matthias; Chowdhury, Debanjan; Sachdev, Subir
  • Nature Physics, Vol. 10, Issue 4
  • DOI: 10.1038/nphys2887

Probing excitations in insulators via injection of spin currents
journal, October 2015


Topological Orders in Rigid States
journal, February 1990


Multiparticle Quantum Mechanics Obeying Fractional Statistics
journal, July 1984


On the theory of identical particles
journal, January 1977

  • Leinaas, J. M.; Myrheim, J.
  • Il Nuovo Cimento B Series 11, Vol. 37, Issue 1
  • DOI: 10.1007/BF02727953

Non-Abelian anyons and topological quantum computation
journal, September 2008


Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet
journal, December 2012

  • Han, Tian-Heng; Helton, Joel S.; Chu, Shaoyan
  • Nature, Vol. 492, Issue 7429
  • DOI: 10.1038/nature11659

Characterizing Topological Order by Studying the Ground States on an Infinite Cylinder
journal, February 2013


Correlators and Fractional Statistics in the Quantum Hall Bulk
journal, November 2007


Disorder-induced Majorana metal in interacting non-Abelian anyon systems
journal, April 2012


Spectroscopy of a topological phase
journal, January 2014


Correlations and beam splitters for quantum Hall anyons
journal, May 2010


Realizing Fractional Chern Insulators in Dipolar Spin Systems
journal, April 2013


Fractional quantum Hall effect in the absence of Landau levels
journal, July 2011

  • Sheng, D. N.; Gu, Zheng-Cheng; Sun, Kai
  • Nature Communications, Vol. 2, Issue 1
  • DOI: 10.1038/ncomms1380

    Figures / Tables found in this record:

      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.