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We study the symmetries of closed Majorana chains in 1+1d, including the translation, fermion parity, spatial parity, and time-reversal symmetries.
1902
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Y.-H. Lin and S.-H. Shao, Anomalies and Bounds on Charged Operators
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D. Stanford and E. Witten, JT gravity and the ensembles of random matrix theory
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W. Ji, S.-H. Shao, and X.-G. Wen, Topological Transition on the Conformal Manifold
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Y.-H. Lin and S.-H. Shao, Duality Defect of the Monster CFT
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M. Baake, P. Chaselon, and M. Schlottmann, The Ising Quantum Chain With Defects. 2. The SO(2n) Kac-Moody Spectra
1989
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1989
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U. Grimm and G. M. Schutz, The Spin 1/2 XXZ Heisenberg chain, the quantum algebra U(q)[sl(2)], and duality transformations for minimal models
1993
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G. Schutz, ’Duality twisted’ boundary conditions in n-state Potts models
1993
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M. Yamanaka, M. Oshikawa, and I. Affleck, Nonperturbative Approach to Luttinger’s Theorem in One Dimension
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1997
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M. Oshikawa, Topological approach to Luttinger’s theorem and the Fermi surface of a Kondo lattice
2000
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M. Oshikawa, Commensurability, excitation gap, and topology in quantum many-particle systems on a periodic lattice
2000
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A. Kitaev, Unpaired Majorana fermions in quantum wires
2001
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V. B. Petkova and J. B. Zuber, Generalized twisted partition functions
2001
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C. H. O. Chui, C. Mercat, W. P. Orrick, and P. A. Pearce, Integrable lattice realizations of conformal twisted boundary conditions
2001
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C.-T. Hsieh, Y. Nakayama, and Y. Tachikawa, Fermionic minimal models
2002
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U. Grimm, Spectrum of a duality twisted Ising quantum chain
2002
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hep-th/0209048
U. Grimm, Duality and conformal twisted boundaries in the Ising model · 2002
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J. Kulp, Two More Fermionic Minimal Models
2003
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M. B. Hastings, Lieb-Schultz-Mattis in Higher Dimensions
2017
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2017
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2017
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A. Kapustin and R. Thorngren, Fermionic SPT phases in higher dimensions and bosonization
2017
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M. A. Metlitski and R. Thorngren, Intrinsic and emergent anomalies at deconfined critical points
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2004
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J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert, Kramers-Wannier duality from conformal defects
2004
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B. Nachtergaele and R. Sims, A multi-dimensional lieb-schultz-mattis theorem
2007
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A. Feiguin, S. Trebst, A. W. W. Ludwig, M. Troyer, A. Kitaev, Z. Wang, and M. H. Freedman, Interacting anyons in topological quantum liquids: The golden chain
2007
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D. Gaiotto and J. Kulp, Orbifold groupoids
2008
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2008
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2010
Cited alongside, same era.
2018
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C.-M. Jian, Z. Bi, and C. Xu, Lieb-Schultz-Mattis theorem and its generalizations from the perspective of the symmetry-protected topological phase
2018
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R. Dijkgraaf and E. Witten, Developments in Topological Gravity
2018
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2018
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M. Cheng, Fermionic Lieb-Schultz-Mattis theorems and weak symmetry-protected phases
2019
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Y. Ogata and H. Tasaki, Lieb–schultz–mattis type theorems for quantum spin chains without continuous symmetry
2019
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Y. Tachikawa, “TASI 2019 Lectures.” https://member.ipmu.jp/yuji.tachikawa/lectures/2019-top-anom
2019
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M. Cheng, Fermionic lieb-schultz-mattis theorems and weak symmetry-protected phases
2019
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W. W. Ho and T. H. Hsieh, Efficient variational simulation of non-trivial quantum states
2019
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2019
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2019
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S. Bachmann, A. Bols, W. De Roeck, and M. Fraas, A many-body index for quantum charge transport
2020
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R. Thorngren, Anomalies and Bosonization
2020
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Y. Ogata, Y. Tachikawa, and H. Tasaki, General Lieb-Schultz-Mattis Type Theorems for Quantum Spin Chains
2021
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O. M. Aksoy, A. Tiwari, and C. Mudry, Lieb-schultz-mattis type theorems for majorana models with discrete symmetries
2021
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D. Delmastro, D. Gaiotto, and J. Gomis, Global anomalies on the Hilbert space
2021
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Y.-H. Lin and S.-H. Shao, ℤ N \mathbb{Z}_{N} symmetries, anomalies, and the modular bootstrap
2021
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2021
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Y. Fukusumi, Y. Tachikawa, and Y. Zheng, Fermionization and boundary states in 1+1 dimensions
2021
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L. Gioia and C. Wang, Nonzero Momentum Requires Long-Range Entanglement
2022
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2022
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C. Cordova, T. T. Dumitrescu, K. Intriligator, and S.-H. Shao, Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond · 2022
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2022
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J. Kaidi, K. Ohmori, and Y. Zheng, Kramers-Wannier-like Duality Defects in (3+1)D Gauge Theories
2022
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2022
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S. Catterall, ’t Hooft anomalies for staggered fermions
2023
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2023
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2023
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