Fetching the paper…
Reading the bibliography…
In quantum spin-1 chains, there is a nonlocal unitary transformation known as the Kennedy-Tasaki transformation $U_{\text{KT}}$, which defines a duality between the Haldane phase and the $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry-breaking phase.
H. A. Kramers and G. H. Wannier, Statistics of the Two-Dimensional Ferromagnet. Part I, Phys. Rev. 60
1941
Earlier work this paper cites.
N. E. Steenrod, Products of cocycles and extensions of mappings, Ann. Math. 48
1947
Earlier work this paper cites.
E. Lieb, T. Schultz, and D. Mattis, Two soluble models of an antiferromagnetic chain, Ann. Phys. 16
1961
Earlier work this paper cites.
R. J. Baxter and S. B. Kelland, Spontaneous polarization of the eight-vertex model, J. Phys. C: Solid State Phys. 7
1974
Earlier work this paper cites.
A. Luther and I. Peschel, Calculation of critical exponents in two dimensions from quantum field theory in one dimension, Phys. Rev. B 12
1975
Earlier work this paper cites.
L. Takhtajan, The picture of low-lying excitations in the isotropic Heisenberg chain of arbitrary spins, Phys. Lett. A 87
1982
Earlier work this paper cites.
H. Babujian, Exact solution of the one-dimensional isotropic Heisenberg chain with arbitrary spins S {S} , Phys. Lett. A 90
1982
Earlier work this paper cites.
I. Affleck and E. H. Lieb, A proof of part of Haldane’s conjecture on spin chains, Lett. Math. Phys. 12
1986
Earlier work this paper cites.
I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Rigorous results on valence-bond ground states in antiferromagnets, Phys. Rev. Lett. 59
1987
Earlier work this paper cites.
C. Hamer, G. Quispel, and M. Batchelor, Conformal anomaly and surface energy for Potts and Ashkin-Teller quantum chains, J. Phys. A: Math. Gen. 20
1987
Earlier work this paper cites.
I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Valence bond ground states in isotropic quantum antiferromagnets, Commun. Math. Phys. 115
1988
Earlier work this paper cites.
M. den Nijs and K. Rommelse, Preroughening transitions in crystal surfaces and valence-bond phases in quantum spin chains, Phys. Rev. B 40
1989
Earlier work this paper cites.
M. Oshikawa, Hidden Z 2 × Z 2 Z_{2}\times Z_{2} symmetry in quantum spin chains with arbitrary integer spin, J. Phys. Condens. Matter 4
1992
Earlier work this paper cites.
T. Kennedy, Non-positive matrix elements for Hamiltonians of spin-1 chains, J. Phys. Condens. Matter 6
1994
Earlier work this paper cites.
A. Kapustin and S. Skorik, Surface excitations and surface energy of the antiferromagnetic XXZ chain by the Bethe ansatz approach, J. Phys. A: Math. Gen. 29
1996
Earlier work this paper cites.
A. Kitazawa and K. Nomura, Bifurcation at the c = 3 / 2 c=3/2 Takhtajan-Babujian point to the c = 1 c=1 critical line, Phys. Rev. B 59
1999
Earlier work this paper cites.
M. Oshikawa, Commensurability, excitation gap, and topology in quantum many-particle systems on a periodic lattice, Phys. Rev. Lett. 84
2000
Earlier work this paper cites.
A. Imambekov, M. Lukin, and E. Demler, Spin-exchange interactions of spin-one bosons in optical lattices: Singlet, nematic, and dimerized phases, Phys. Rev. A 68
2003
Earlier work this paper cites.
S. Lukyanov and V. Terras, Long-distance asymptotics of spin–spin correlation functions for the XXZ spin chain, Nucl. Phys. B 654
2003
Earlier work this paper cites.
J. Oitmaa and A. M. A. von Brasch, Spin-1 Ising model in a transverse crystal field, Phys. Rev. B 67
2003
Earlier work this paper cites.
A. Läuchli, G. Schmid, and S. Trebst, Spin nematics correlations in bilinear-biquadratic S = 1 S=1 spin chains, Phys. Rev. B 74
2006
Earlier work this paper cites.
D. Pérez-García, M. M. Wolf, M. Sanz, F. Verstraete, and J. I. Cirac, String order and symmetries in quantum spin lattices, Phys. Rev. Lett. 100
2008
Earlier work this paper cites.
H.-H. Tu, G.-M. Zhang, and T. Xiang, Class of exactly solvable SO( n n ) symmetric spin chains with matrix product ground states, Phys. Rev. B 78
2008
Earlier work this paper cites.
Z. Yang, L. Yang, J. Dai, and T. Xiang, Rigorous solution of the spin-1 quantum ising model with single-ion anisotropy, Phys. Rev. Lett. 100
2008
Earlier work this paper cites.
Z.-C. Gu and X.-G. Wen, Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order, Phys. Rev. B 80
2009
Earlier work this paper cites.
F. Pollmann, A. M. Turner, E. Berg, and M. Oshikawa, Entanglement spectrum of a topological phase in one dimension, Phys. Rev. B 81
2010
Cited alongside, same era.
X. Chen, Z.-C. Gu, and X.-G. Wen, Classification of gapped symmetric phases in one-dimensional spin systems, Phys. Rev. B 83
2011
Cited alongside, same era.
K. Okunishi, Topological disentangler for the valence-bond-solid chain, Phys. Rev. B 83
2011
Cited alongside, same era.
W. Son, L. Amico, R. Fazio, A. Hamma, S. Pascazio, and V. Vedral, Quantum phase transition between cluster and antiferromagnetic states, EPL 95
2011
Cited alongside, same era.
F. Pollmann, E. Berg, A. M. Turner, and M. Oshikawa, Symmetry protection of topological phases in one-dimensional quantum spin systems, Phys. Rev. B 85
2012
Cited alongside, same era.
D. E. Parker, T. Scaffidi, and R. Vasseur, Topological Luttinger liquids from decorated domain walls, Phys. Rev. B 97
2018
Later among the works it cites.
M. A. Metlitski and R. Thorngren, Intrinsic and emergent anomalies at deconfined critical points, Phys. Rev. B 98
2018
Later among the works it cites.
J. Wang, X.-G. Wen, and E. Witten, Symmetric gapped interfaces of SPT and SET states: Systematic constructions, Phys. Rev. X 8
2018
Later among the works it cites.
A. Prakash, J. Wang, and T.-C. Wei, Unwinding short-range entanglement, Phys. Rev. B 98
2018
Later among the works it cites.
R. Thorngren and D. V. Else, Gauging spatial symmetries and the classification of topological crystalline phases, Phys. Rev. X 8
2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
X. Chen, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, Symmetry-protected topological orders in interacting bosonic systems, Science 338
2012
Cited alongside, same era.
F. Pollmann and A. M. Turner, Detection of symmetry-protected topological phases in one dimension, Phys. Rev. B 86
2012
Cited alongside, same era.
P. Di Francesco, P. Mathieu, and D. Sénéchal, Conformal Field Theory (Springer Science & Business Media, New York, 2012)
2012
Cited alongside, same era.
X. Chen, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, Symmetry protected topological orders and the group cohomology of their symmetry group, Phys. Rev. B 87
2013
Cited alongside, same era.
D. V. Else, S. D. Bartlett, and A. C. Doherty, Hidden symmetry-breaking picture of symmetry-protected topological order, Phys. Rev. B 88
2013
Cited alongside, same era.
K. Duivenvoorden and T. Quella, From symmetry-protected topological order to Landau order, Phys. Rev. B 88
2013
Cited alongside, same era.
K. Okunishi and K. Harada, Symmetry-protected topological order and negative-sign problem for SO ( N ) \mathrm{SO(}N) bilinear-biquadratic chains, Phys. Rev. B 89
2014
Cited alongside, same era.
B. Zeng, X. Chen, D.-L. Zhou, and X.-G. Wen, Quantum Information Meets Quantum Matter (Springer, New York, 2019)
2019
Later among the works it cites.
N. G. Jones and R. Verresen, Asymptotic correlations in gapped and critical topological phases of 1D quantum systems, J. Stat. Phys. 175
2019
Later among the works it cites.
Y. Ogata and H. Tasaki, Lieb–Schultz–Mattis type theorems for quantum spin chains without continuous symmetry, Commun. Math. Phys. 372
2019
Later among the works it cites.
Y. Yao, C.-T. Hsieh, and M. Oshikawa, Anomaly matching and symmetry-protected critical phases in S U ( N ) SU(N) spin systems in 1 + 1 1+1 dimensions, Phys. Rev. Lett. 123
2019
Later among the works it cites.
E. O’Brien and P. Fendley, Self-dual S 3 S_{3} -invariant quantum chains, SciPost Phys. 9
2020
Later among the works it cites.
2020
Later among the works it cites.
H. Tasaki, Physics and Mathematics of Quantum Many-Body Systems (Springer, New York, 2020)
2020
Later among the works it cites.
Y. Tachikawa, On gauging finite subgroups, SciPost Phys. 8
2020
Later among the works it cites.
R. Verresen, R. Thorngren, N. G. Jones, and F. Pollmann, Gapless topological phases and symmetry-enriched quantum criticality, Phys. Rev. X 11
2021
Later among the works it cites.
C. M. Duque, H.-Y. Hu, Y.-Z. You, V. Khemani, R. Verresen, and R. Vasseur, Topological and symmetry-enriched random quantum critical points, Phys. Rev. B 103
2021
Later among the works it cites.
R. Thorngren, A. Vishwanath, and R. Verresen, Intrinsically gapless topological phases, Phys. Rev. B 104
2021
Later among the works it cites.
D.-C. Lu, C. Xu, and Y.-Z. You, Self-duality protected multicriticality in deconfined quantum phase transitions, Phys. Rev. B 104
2021
Later among the works it cites.
2021
Later among the works it cites.
H. Yang, H. Nakano, and H. Katsura, Symmetry-protected topological phases in spinful bosons with a flat band, Phys. Rev. Research 3
2021
Later among the works it cites.
Y. Ogata, Y. Tachikawa, and H. Tasaki, General Lieb–Schultz–Mattis type theorems for quantum spin chains, Commun. Math. Phys. 385
2021
Later among the works it cites.
Y. Yao and M. Oshikawa, Twisted boundary condition and Lieb–Schultz–Mattis ingappability for discrete symmetries, Phys. Rev. Lett. 126
2021
Later among the works it cites.
L. Zou, Y.-C. He, and C. Wang, Stiefel liquids: Possible non-Lagrangian quantum criticality from intertwined orders, Phys. Rev. X 11
2021
Later among the works it cites.
2021
Later among the works it cites.