Non-abelian bosonization in two and three spatial dimensions and applications
Abstract
In this paper, we generalize Witten's non-abelian bosonization in (1+1)-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. We apply the bosonization results to the SU(2) gauge theory of the π-flux phase, critical spin liquids in 1,2,3 spatial dimensions, and twisted bilayer graphene.
- Authors:
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), High Energy Physics (HEP); USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
- OSTI Identifier:
- 1822580
- Alternate Identifier(s):
- OSTI ID: 1901545
- Grant/Contract Number:
- AC02-05-CH11231; KC2301; AC02-05CH11231
- Resource Type:
- Published Article
- Journal Name:
- Nuclear Physics. B
- Additional Journal Information:
- Journal Name: Nuclear Physics. B Journal Volume: 972 Journal Issue: C; Journal ID: ISSN 0550-3213
- Publisher:
- Elsevier
- Country of Publication:
- Netherlands
- Language:
- English
- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Citation Formats
Huang, Yen-Ta, and Lee, Dung-Hai. Non-abelian bosonization in two and three spatial dimensions and applications. Netherlands: N. p., 2021.
Web. doi:10.1016/j.nuclphysb.2021.115565.
Huang, Yen-Ta, & Lee, Dung-Hai. Non-abelian bosonization in two and three spatial dimensions and applications. Netherlands. https://doi.org/10.1016/j.nuclphysb.2021.115565
Huang, Yen-Ta, and Lee, Dung-Hai. Mon .
"Non-abelian bosonization in two and three spatial dimensions and applications". Netherlands. https://doi.org/10.1016/j.nuclphysb.2021.115565.
@article{osti_1822580,
title = {Non-abelian bosonization in two and three spatial dimensions and applications},
author = {Huang, Yen-Ta and Lee, Dung-Hai},
abstractNote = {In this paper, we generalize Witten's non-abelian bosonization in (1+1)-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. We apply the bosonization results to the SU(2) gauge theory of the π-flux phase, critical spin liquids in 1,2,3 spatial dimensions, and twisted bilayer graphene.},
doi = {10.1016/j.nuclphysb.2021.115565},
journal = {Nuclear Physics. B},
number = C,
volume = 972,
place = {Netherlands},
year = {2021},
month = {11}
}
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1016/j.nuclphysb.2021.115565
https://doi.org/10.1016/j.nuclphysb.2021.115565
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene
journal, October 2019
- Lu, Xiaobo; Stepanov, Petr; Yang, Wei
- Nature, Vol. 574, Issue 7780
Evidence for Deconfined Quantum Criticality in a Two-Dimensional Heisenberg Model with Four-Spin Interactions
journal, June 2007
- Sandvik, Anders W.
- Physical Review Letters, Vol. 98, Issue 22
Unconventional superconductivity in magic-angle graphene superlattices
journal, March 2018
- Cao, Yuan; Fatemi, Valla; Fang, Shiang
- Nature, Vol. 556, Issue 7699
Intrinsic quantized anomalous Hall effect in a moiré heterostructure
journal, December 2019
- Serlin, M.; Tschirhart, C. L.; Polshyn, H.
- Science, Vol. 367, Issue 6480
Competing orders, nonlinear sigma models, and topological terms in quantum magnets
journal, August 2006
- Senthil, T.; Fisher, Matthew P. A.
- Physical Review B, Vol. 74, Issue 6
Anomalies and fermion zero modes on strings and domain walls
journal, January 1985
- Callan, C. G.; Harvey, J. A.
- Nuclear Physics B, Vol. 250, Issue 1-4
Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
journal, July 2019
- Sharpe, Aaron L.; Fox, Eli J.; Barnard, Arthur W.
- Science, Vol. 365, Issue 6453
The Stable Homotopy of the Classical Groups
journal, September 1959
- Bott, Raoul
- The Annals of Mathematics, Vol. 70, Issue 2
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
New approach to the mixed-valence problem
journal, March 1984
- Coleman, Piers
- Physical Review B, Vol. 29, Issue 6
Superconductivity, correlated insulators, and Wess–Zumino–Witten terms in twisted bilayer graphene
journal, November 2020
- Christos, Maine; Sachdev, Subir; Scheurer, Mathias S.
- Proceedings of the National Academy of Sciences, Vol. 117, Issue 47
Gapped symmetry preserving surface state for the electron topological insulator
journal, September 2013
- Wang, Chong; Potter, Andrew C.; Senthil, T.
- Physical Review B, Vol. 88, Issue 11
Antiferromagnetism. Theory of Superexchange Interaction
journal, July 1950
- Anderson, P. W.
- Physical Review, Vol. 79, Issue 2
Quantum sine-Gordon equation as the massive Thirring model
journal, April 1975
- Coleman, Sidney
- Physical Review D, Vol. 11, Issue 8
Critical theory of quantum spin chains
journal, October 1987
- Affleck, Ian; Haldane, F. D. M.
- Physical Review B, Vol. 36, Issue 10
�ber die Abbildungen der dreidimensionalen Sph�re auf die Kugelfl�che
journal, December 1931
- Hopf, Heinz
- Mathematische Annalen, Vol. 104, Issue 1
Cascade of phase transitions and Dirac revivals in magic-angle graphene
journal, June 2020
- Zondiner, U.; Rozen, A.; Rodan-Legrain, D.
- Nature, Vol. 582, Issue 7811
O(3) Nonlinear Model and the Topological Distinction between Integer- and Half-Integer-Spin Antiferromagnets in Two Dimensions
journal, August 1988
- Haldane, F. D. M.
- Physical Review Letters, Vol. 61, Issue 8
Periodic table for topological insulators and superconductors
conference, January 2009
- Kitaev, Alexei; Lebedev, Vladimir; Feigel’man, Mikhail
- ADVANCES IN THEORETICAL PHYSICS: Landau Memorial Conference, AIP Conference Proceedings
A PCAC puzzle: π0→γγ in the σ-model
journal, March 1969
- Bell, J. S.; Jackiw, R.
- Il Nuovo Cimento A, Vol. 60, Issue 1
Non perturbative anomalies in higher dimensions
journal, September 1984
- Elitzur, S.; Nair, V. P.
- Nuclear Physics B, Vol. 243, Issue 2
Global aspects of current algebra
journal, August 1983
- Witten, Edward
- Nuclear Physics B, Vol. 223, Issue 2
Gauge Noninvariance and Parity Nonconservation of Three-Dimensional Fermions
journal, January 1984
- Redlich, A. N.
- Physical Review Letters, Vol. 52, Issue 1
Theta-terms in nonlinear sigma-models
journal, March 2000
- Abanov, A. G.; Wiegmann, P. B.
- Nuclear Physics B, Vol. 570, Issue 3
SU(2) gauge invariance and order parameters in strongly coupled electronic systems
journal, August 1988
- Dagotto, Elbio; Fradkin, Eduardo; Moreo, Adriana
- Physical Review B, Vol. 38, Issue 4
Exact Solution of a Many‐Fermion System and Its Associated Boson Field
journal, February 1965
- Mattis, Daniel C.; Lieb, Elliott H.
- Journal of Mathematical Physics, Vol. 6, Issue 2
Topological insulators and superconductors: tenfold way and dimensional hierarchy
journal, June 2010
- Ryu, Shinsei; Schnyder, Andreas P.; Furusaki, Akira
- New Journal of Physics, Vol. 12, Issue 6
Hopf term induced by fermions
journal, January 2000
- Abanov, Alexander G.
- Physics Letters B, Vol. 492, Issue 3-4
Linking Numbers, Spin, and Statistics of Solitons
journal, December 1983
- Wilczek, Frank; Zee, A.
- Physical Review Letters, Vol. 51, Issue 25
Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State
journal, April 1983
- Haldane, F. D. M.
- Physical Review Letters, Vol. 50, Issue 15
Non-Abelian anomaly and vector-meson decays
journal, August 1984
- Kaymakcalan, Ö.; Rajeev, S.; Schechter, J.
- Physical Review D, Vol. 30, Issue 3
Parity violation and gauge noninvariance of the effective gauge field action in three dimensions
journal, May 1984
- Redlich, A. N.
- Physical Review D, Vol. 29, Issue 10
Anomalous Ward Identities in Spinor Field Theories
journal, August 1969
- Bardeen, William A.
- Physical Review, Vol. 184, Issue 5
Soliton operators for the quantized sine-Gordon equation
journal, May 1975
- Mandelstam, S.
- Physical Review D, Vol. 11, Issue 10
Valence-bond and spin-Peierls ground states of low-dimensional quantum antiferromagnets
journal, April 1989
- Read, N.; Sachdev, Subir
- Physical Review Letters, Vol. 62, Issue 14
Cascade of electronic transitions in magic-angle twisted bilayer graphene
journal, June 2020
- Wong, Dillon; Nuckolls, Kevin P.; Oh, Myungchul
- Nature, Vol. 582, Issue 7811
Spin liquid ground state of the spin- square - Heisenberg model
journal, July 2012
- Jiang, Hong-Chen; Yao, Hong; Balents, Leon
- Physical Review B, Vol. 86, Issue 2
Large- n limit of the Heisenberg-Hubbard model: Implications for high- superconductors
journal, March 1988
- Affleck, Ian; Marston, J. Brad
- Physical Review B, Vol. 37, Issue 7
Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators
journal, June 2016
- Metlitski, Max A.; Vishwanath, Ashvin
- Physical Review B, Vol. 93, Issue 24
Square-Lattice Algebraic Spin Liquid with SO(5) Symmetry
journal, April 2008
- Xu, Cenke; Sachdev, Subir
- Physical Review Letters, Vol. 100, Issue 13
Calculation of critical exponents in two dimensions from quantum field theory in one dimension
journal, November 1975
- Luther, A.; Peschel, I.
- Physical Review B, Vol. 12, Issue 9
Axial-Vector Vertex in Spinor Electrodynamics
journal, January 1969
- Adler, Stephen L.
- Physical Review, Vol. 177, Issue 5
Moire bands in twisted double-layer graphene
journal, July 2011
- Bistritzer, R.; MacDonald, A. H.
- Proceedings of the National Academy of Sciences, Vol. 108, Issue 30
The Stable Homotopy of the Classical Groups
journal, October 1957
- Bott, R.
- Proceedings of the National Academy of Sciences, Vol. 43, Issue 10
A holographic theory for the phase transitions between fermionic symmetry-protected topological states
journal, December 2019
- Tsui, Lokman; Huang, Yen-Ta; Lee, Dung-Hai
- Nuclear Physics B, Vol. 949
Correlated insulator behaviour at half-filling in magic-angle graphene superlattices
journal, March 2018
- Cao, Yuan; Fatemi, Valla; Demir, Ahmet
- Nature, Vol. 556, Issue 7699
Tuning superconductivity in twisted bilayer graphene
journal, January 2019
- Yankowitz, Matthew; Chen, Shaowen; Polshyn, Hryhoriy
- Science, Vol. 363, Issue 6431
Many-Body Spin Berry Phases Emerging from the -Flux State: Competition between Antiferromagnetism and the Valence-Bond-Solid State
journal, July 2005
- Tanaka, Akihiro; Hu, Xiao
- Physical Review Letters, Vol. 95, Issue 3
Doping a Mott insulator: Physics of high-temperature superconductivity
journal, January 2006
- Lee, Patrick A.; Nagaosa, Naoto; Wen, Xiao-Gang
- Reviews of Modern Physics, Vol. 78, Issue 1
Reflection positivity and invertible topological phases
journal, January 2021
- Freed, Daniel S.; Hopkins, Michael J.
- Geometry & Topology, Vol. 25, Issue 3
Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model
journal, February 1983
- Haldane, F. D. M.
- Physics Letters A, Vol. 93, Issue 9
Plaquette Ordered Phase and Quantum Phase Diagram in the Spin- Square Heisenberg Model
journal, July 2014
- Gong, Shou-Shu; Zhu, Wei; Sheng, D. N.
- Physical Review Letters, Vol. 113, Issue 2
Non-abelian bosonization in two dimensions
journal, December 1984
- Witten, Edward
- Communications in Mathematical Physics, Vol. 92, Issue 4
Effects of interactions on the topological classification of free fermion systems
journal, April 2010
- Fidkowski, Lukasz; Kitaev, Alexei
- Physical Review B, Vol. 81, Issue 13
The “non-regularizability” of gapless free fermion Hamiltonian protected by on-site symmetries
journal, May 2020
- Huang, Yen-Ta; Tsui, Lokman; Lee, Dung-Hai
- Nuclear Physics B, Vol. 954
Exact diagonalization of finite frustrated spin-(1/2 Heisenberg models
journal, March 1990
- Figueirido, F.; Karlhede, A.; Kivelson, S.
- Physical Review B, Vol. 41, Issue 7
Current algebra, baryons, and quark confinement
journal, August 1983
- Witten, Edward
- Nuclear Physics B, Vol. 223, Issue 2