Statistics of Fractionalized Excitations through Threshold Spectroscopy

Morampudi, Siddhardh C.; Turner, Ari M.; Pollmann, Frank; Wilczek, Frank

doi:10.1103/physrevlett.118.227201

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:

Morampudi, Siddhardh C. ^[1]; Turner, Ari M. ^[2]; Pollmann, Frank ^[3]; Wilczek, Frank ^[4]

Max-Planck-Inst. für Physik komplexer Systeme, Dresden (Germany)
Technion-Israel Inst. of Tech., Haifa (Israel); Johns Hopkins Univ., Baltimore, MD (United States)
Max-Planck-Inst. für Physik komplexer Systeme, Dresden (Germany); Technische Univ. Munchen, Garching (Germany)
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:: 2017-05-31

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)

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.

Copy to clipboard


                    Morampudi, Siddhardh C., Turner, Ari M., Pollmann, Frank, & Wilczek, Frank. Statistics of Fractionalized Excitations through Threshold Spectroscopy.  United States.  doi:https://doi.org/10.1103/physrevlett.118.227201

Copy to clipboard


                    Morampudi, Siddhardh C., Turner, Ari M., Pollmann, Frank, and Wilczek, Frank. Wed .  
        "Statistics of Fractionalized Excitations through Threshold Spectroscopy".  United States.  doi:https://doi.org/10.1103/physrevlett.118.227201.  https://www.osti.gov/servlets/purl/1505576.

Copy to clipboard


                    
@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}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

DOI: https://doi.org/10.1103/physrevlett.118.227201

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 18 works

Citation information provided by
Web of Science

Figures / Tables:

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.

All figures and tables (2 total)

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Classifying fractionalization: Symmetry classification of gapped $Z_{2}$ spin liquids in two dimensions
journal, March 2013

Essin, Andrew M.; Hermele, Michael
Physical Review B, Vol. 87, Issue 10
DOI: 10.1103/PhysRevB.87.104406

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

Halperin, B. I.
Physical Review Letters, Vol. 52, Issue 18
DOI: 10.1103/PhysRevLett.52.1583

Quantum orders and symmetric spin liquids
journal, April 2002

Wen, Xiao-Gang
Physical Review B, Vol. 65, Issue 16
DOI: 10.1103/PhysRevB.65.165113

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

Moessner, R.; Sondhi, S. L.
Physical Review Letters, Vol. 86, Issue 9
DOI: 10.1103/PhysRevLett.86.1881

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

Kalmeyer, V.; Laughlin, R. B.
Physical Review Letters, Vol. 59, Issue 18
DOI: 10.1103/PhysRevLett.59.2095

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

Wigner, Eugene P.
Physical Review, Vol. 73, Issue 9
DOI: 10.1103/PhysRev.73.1002

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

Zaletel, Michael P.; Mong, Roger S. K.; Pollmann, Frank
Physical Review Letters, Vol. 110, Issue 23
DOI: 10.1103/PhysRevLett.110.236801

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

Wilczek, Frank
Physical Review Letters, Vol. 48, Issue 17
DOI: 10.1103/PhysRevLett.48.1144

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

Yang, Kun; Halperin, Bertrand I.
Physical Review B, Vol. 79, Issue 11
DOI: 10.1103/PhysRevB.79.115317

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

Mashkevich, Stefan; Myrheim, Jan; Olaussen, Kåre
Physics Letters B, Vol. 348, Issue 3-4
DOI: 10.1016/0370-2693(95)00139-C

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

Goldman, Nathan; Beugnon, Jérôme; Gerbier, Fabrice
Physical Review Letters, Vol. 108, Issue 25
DOI: 10.1103/PhysRevLett.108.255303

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

Dodds, Tyler; Bhattacharjee, Subhro; Kim, Yong Baek
Physical Review B, Vol. 88, Issue 22
DOI: 10.1103/PhysRevB.88.224413

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

Levin, Michael; Wen, Xiao-Gang
Physical Review Letters, Vol. 96, Issue 11
DOI: 10.1103/PhysRevLett.96.110405

Topological Entanglement Entropy
journal, March 2006

Kitaev, Alexei; Preskill, John
Physical Review Letters, Vol. 96, Issue 11
DOI: 10.1103/PhysRevLett.96.110404

Dynamics and Transport of the $Z_{2}$ Spin Liquid: Application to $κ − (ET)_{2} {Cu}_{2} (CN)_{3}$
journal, April 2009

Qi, Yang; Xu, Cenke; Sachdev, Subir
Physical Review Letters, Vol. 102, Issue 17
DOI: 10.1103/PhysRevLett.102.176401

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

Camino, F. E.; Zhou, Wei; Goldman, V. J.
Physical Review B, Vol. 72, Issue 7
DOI: 10.1103/PhysRevB.72.075342

Quantum Mechanics of Fractional-Spin Particles
journal, October 1982

Wilczek, Frank
Physical Review Letters, Vol. 49, Issue 14
DOI: 10.1103/PhysRevLett.49.957

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

Kagome´- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons
journal, June 1992

Sachdev, Subir
Physical Review B, Vol. 45, Issue 21
DOI: 10.1103/PhysRevB.45.12377

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

Cooper, N. R.; Stern, Ady
Physical Review Letters, Vol. 102, Issue 17
DOI: 10.1103/PhysRevLett.102.176807

Statistical mechanics of anyons
journal, January 1985

Arovas, Daniel P.; Schrieffer, Robert; Wilczek, Frank
Nuclear Physics B, Vol. 251
DOI: 10.1016/0550-3213(85)90252-4

Flux quantization for semions on a torus
journal, November 1993

Kallin, C.
Physical Review B, Vol. 48, Issue 18
DOI: 10.1103/PhysRevB.48.13742

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

Zhang, Yi; Grover, Tarun; Turner, Ari
Physical Review B, Vol. 85, Issue 23
DOI: 10.1103/PhysRevB.85.235151

Anyons on a torus
journal, October 1990

Wen, X. G.; Dagotto, E.; Fradkin, E.
Physical Review B, Vol. 42, Issue 10
DOI: 10.1103/PhysRevB.42.6110

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

Anderson, P. W.
Science, Vol. 235, Issue 4793
DOI: 10.1126/science.235.4793.1196

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

Moradi, Heidar; Wen, Xiao-Gang
Physical Review Letters, Vol. 115, Issue 3
DOI: 10.1103/PhysRevLett.115.036802

Adiabatic Cooling with Non-Abelian Anyons
journal, August 2010

Gervais, G.; Yang, Kun
Physical Review Letters, Vol. 105, Issue 8
DOI: 10.1103/PhysRevLett.105.086801

Fractional statistics on a torus
journal, April 1990

Einarsson, Torbjörn
Physical Review Letters, Vol. 64, Issue 17
DOI: 10.1103/PhysRevLett.64.1995

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

Chen, Xie; Gu, Zheng-Cheng; Wen, Xiao-Gang
Physical Review B, Vol. 82, Issue 15
DOI: 10.1103/PhysRevB.82.155138

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

Read, N.; Chakraborty, B.
Physical Review B, Vol. 40, Issue 10
DOI: 10.1103/PhysRevB.40.7133

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

Neupert, Titus; Santos, Luiz; Chamon, Claudio
Physical Review Letters, Vol. 106, Issue 23
DOI: 10.1103/PhysRevLett.106.236804

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

Tsui, D. C.; Stormer, H. L.; Gossard, A. C.
Physical Review Letters, Vol. 48, Issue 22
DOI: 10.1103/PhysRevLett.48.1559

High-Temperature Fractional Quantum Hall States
journal, June 2011

Tang, Evelyn; Mei, Jia-Wei; Wen, Xiao-Gang
Physical Review Letters, Vol. 106, Issue 23
DOI: 10.1103/PhysRevLett.106.236802

Spin liquids in frustrated magnets
journal, March 2010

Balents, Leon
Nature, Vol. 464, Issue 7286
DOI: 10.1038/nature08917

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

Ben-Shach, G.; Laumann, C. R.; Neder, I.
Physical Review Letters, Vol. 110, Issue 10
DOI: 10.1103/PhysRevLett.110.106805

Chiral spin states and superconductivity
journal, June 1989

Wen, X. G.; Wilczek, Frank; Zee, A.
Physical Review B, Vol. 39, Issue 16
DOI: 10.1103/PhysRevB.39.11413

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

Chatterjee, Shubhayu; Sachdev, Subir
Physical Review B, Vol. 92, Issue 16
DOI: 10.1103/PhysRevB.92.165113

Topological Orders in Rigid States
journal, February 1990

Wen, X. G.
International Journal of Modern Physics B, Vol. 04, Issue 02
DOI: 10.1142/S0217979290000139

Multiparticle Quantum Mechanics Obeying Fractional Statistics
journal, July 1984

Wu, Yong-Shi
Physical Review Letters, Vol. 53, Issue 2
DOI: 10.1103/PhysRevLett.53.111

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

Nayak, Chetan; Simon, Steven H.; Stern, Ady
Reviews of Modern Physics, Vol. 80, Issue 3
DOI: 10.1103/RevModPhys.80.1083

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

Cincio, L.; Vidal, G.
Physical Review Letters, Vol. 110, Issue 6
DOI: 10.1103/PhysRevLett.110.067208

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

Vishveshwara, Smitha; Stone, Michael; Sen, Diptiman
Physical Review Letters, Vol. 99, Issue 19
DOI: 10.1103/PhysRevLett.99.190401

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

Laumann, Chris R.; Ludwig, Andreas W. W.; Huse, David A.
Physical Review B, Vol. 85, Issue 16
DOI: 10.1103/PhysRevB.85.161301

Spectroscopy of a topological phase
journal, January 2014

Kamfor, Michael; Dusuel, Sébastien; Vidal, Julien
Physical Review B, Vol. 89, Issue 4
DOI: 10.1103/PhysRevB.89.045411

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

Vishveshwara, Smitha; Cooper, N. R.
Physical Review B, Vol. 81, Issue 20
DOI: 10.1103/PhysRevB.81.201306

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

Yao, N. Y.; Gorshkov, A. V.; Laumann, C. R.
Physical Review Letters, Vol. 110, Issue 18
DOI: 10.1103/PhysRevLett.110.185302

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

Works referencing / citing this record:

A quantum dipolar spin liquid
journal, February 2018

Yao, N. Y.; Zaletel, M. P.; Stamper-Kurn, D. M.
Nature Physics, Vol. 14, Issue 4
DOI: 10.1038/s41567-017-0030-7

Flux-driven quantum spin liquids in kagome optical lattices
journal, November 2019

Hui, Hoi-Yin; Chen, Mengsu; Tewari, Sumanta
Physical Review A, Vol. 100, Issue 5
DOI: 10.1103/physreva.100.053614

Dynamical and topological properties of the Kitaev model in a [111] magnetic field
journal, July 2018

Gohlke, Matthias; Moessner, Roderich; Pollmann, Frank
Physical Review B, Vol. 98, Issue 1
DOI: 10.1103/physrevb.98.014418

Diagnosing Fractionalization from the Spin Dynamics of $Z_{2}$ Spin Liquids on the Kagome Lattice by Quantum Monte Carlo Simulations
journal, August 2018

Becker, Jonas; Wessel, Stefan
Physical Review Letters, Vol. 121, Issue 7
DOI: 10.1103/physrevlett.121.077202

Spectroscopy of Spinons in Coulomb Quantum Spin Liquids
journal, March 2020

Morampudi, Siddhardh C.; Wilczek, Frank; Laumann, Chris R.
Physical Review Letters, Vol. 124, Issue 9
DOI: 10.1103/physrevlett.124.097204

Figures / Tables found in this record:

FIG. 1 (p. 3)

FIG. 2 (p. 5)

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

Similar Records in DOE PAGES and OSTI.GOV collections:

Spectroscopy of a tunable moiré system with a correlated and topological flat band

Journal Article Liu, Xiaomeng ; Chiu, Cheng-Li ; Lee, Jong Yeon ; ... - Nature Communications

Abstract Moiré superlattices created by the twisted stacking of two-dimensional crystals can host electronic bands with flat energy dispersion in which enhanced interactions promote correlated electron states. The twisted double bilayer graphene (TDBG), where two Bernal bilayer graphene are stacked with a twist angle, is such a moiré system with tunable flat bands. Here, we use gate-tuned scanning tunneling spectroscopy to directly demonstrate the tunability of the band structure of TDBG with an electric field and to show spectroscopic signatures of electronic correlations and topology for its flat band. Our spectroscopic experiments are in agreement with a continuum model ofmore »« less
DOI: https://doi.org/10.1038/s41467-021-23031-0
Fractional statistics from gravitation

Journal Article Cho, Y M ; Park, D H - Physical Review, D (Particles Fields); (United States)

We show that the solitons of the SO(3) nonlinear sigma model in 2+1 dimensions, when coupled to gravitation with the gravitational Chern-Simons interaction, become anyons in the absence of the Hopf term. In particular we calculate the fractional statistical factor of the gravitating anyons, and prove that the gravitational Chern-Simons term itself can be interpreted as the Hopf term of the topological current of [Pi][sub 2]([ital S][sup 2]).
DOI: https://doi.org/10.1103/PhysRevD.49.R6269
Anomalous Crystal Symmetry Fractionalization on the Surface of Topological Crystalline Insulators

Journal Article Qi, Yang ; Fu, Liang - Physical Review Letters

The surface of a three-dimensional topological electron system often hosts symmetry-protected gapless surface states. With the effect of electron interactions, these surface states can be gapped out without symmetry breaking by a surface topological order, in which the anyon excitations carry anomalous symmetry fractionalization that cannot be realized in a genuine two-dimensional system. We show here that for a mirror-symmetry-protected topological crystalline insulator with mirror Chern numbermore »« less
Cited by 9
DOI: https://doi.org/10.1103/physrevlett.115.236801

Full Text Available
Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model

Journal Article Gong, Shou-Shu ; Zhu, Wei ; Sheng, D. N. - Scientific Reports

The fractional quantum Hall effect (FQHE) realized in two-dimensional electron systems under a magnetic field is one of the most remarkable discoveries in condensed matter physics. Interestingly, it has been proposed that FQHE can also emerge in time-reversal invariant spin systems, known as the chiral spin liquid (CSL) characterized by the topological order and the emerging of the fractionalized quasiparticles. A CSL can naturally lead to the exotic superconductivity originating from the condense of anyonic quasiparticles. Although CSL was highly sought after for more than twenty years, it had never been found in a spin isotropic Heisenberg model or related materials. By developing a density-matrix renormalization group based method for adiabatically inserting flux, we discover a FQHE in a spin-more »« less
DOI: https://doi.org/10.1038/srep06317

Full Text Available
Investigations of surface structural, dynamical, and magnetic properties of systems exhibiting multiferroicity, and topological phases by helium scattering spectroscopies

Technical Report El-Batanouny, Maged

We propose to investigate the surface structural, dynamics and magnetic properties of the novel class of topological insulator crystals, as well as crystals that exhibit multiferroicity, magnetoelectricity and thermoelectricity. Topological insulators (TIs) are a new class of insulators in which a bulk gap for electronic excitations is generated because of the strong spin-orbit coupling inherent to these systems. These materials are distinguished from ordinary insulators by the presence of gapless metallic surface states, resembling chiral edge modes in quantum Hall systems, but with unconventional spin textures. These exotic metallic states are formed by topological conditions that also render the electrons travelling on such surfaces insensitive to scattering by impurities. The electronic quasi-particles populating the topological surface state are Dirac fermions; they have a linear dispersion and thus are massless just like photons. We propose to investigate the interaction of these massless Dirac fermions with the massive lattice in the newly discovered crystals, Bi2Se3, Bi2Te3 and Sb2Te3. We shall use inelastic helium beam scattering from surfaces to search for related signatures in surface phonon dispersions mappings that cover the entire surface Brillouin zone of these materials. Our recent investigations of the (001) surface of the multiferroic crystals (Li/Na)Cu2O2 revealed an anomalous surface structural behavior where surface Cumore »« less
DOI: https://doi.org/10.2172/1206408

Full Text Available

Similar Records

Title: Statistics of Fractionalized Excitations through Threshold Spectroscopy

Abstract

Citation Formats

Figures / Tables:

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

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

Kagome´- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons journal, June 1992

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

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

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

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

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

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

A quantum dipolar spin liquid journal, February 2018

Flux-driven quantum spin liquids in kagome optical lattices journal, November 2019

Dynamical and topological properties of the Kitaev model in a [111] magnetic field journal, July 2018

Diagnosing Fractionalization from the Spin Dynamics of Z 2 Spin Liquids on the Kagome Lattice by Quantum Monte Carlo Simulations journal, August 2018

Spectroscopy of Spinons in Coulomb Quantum Spin Liquids journal, March 2020

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

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

Kagome´- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons
journal, June 1992

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

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

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

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

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

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

A quantum dipolar spin liquid
journal, February 2018

Flux-driven quantum spin liquids in kagome optical lattices
journal, November 2019

Dynamical and topological properties of the Kitaev model in a [111] magnetic field
journal, July 2018

Diagnosing Fractionalization from the Spin Dynamics of $Z_{2}$ Spin Liquids on the Kagome Lattice by Quantum Monte Carlo Simulations
journal, August 2018

Spectroscopy of Spinons in Coulomb Quantum Spin Liquids
journal, March 2020