Symmetry protected topological phases beyond groups: The q-deformed bilinear-biquadratic spin chain

X.-H. Chen, I. McCulloch, M. T. Batchelor, and H.-Q. Zhou, Symmetry-protected trivial phases and quantum phase transitions in an anisotropic antiferromagnetic spin-1 biquadratic model, Phys. Rev. B102

Original

1912

Earlier work this paper cites.

G. V. Uimin, One-dimensional problem for s = 1 with modified antiferromagnetic Hamiltonian, JETP Lett. 12

1970

Earlier work this paper cites.

C. K. Lai, Lattice gas with nearest-neighbor interaction in one dimension with arbitrary statistics, J. Math. Phys. 15

1974

Earlier work this paper cites.

B. Sutherland, Model for a multicomponent quantum system, Phys. Rev. B12

1975

Earlier work this paper cites.

L. Tagliacozzo, T. R. de Oliveira, S. Iblisdir, and J. I. Latorre, Scaling of entanglement support for matrix product states, Phys. Rev. B78

Original

1976

Earlier work this paper cites.

A. Zamolodchikov and V. Fateev, Model factorized S matrix and an integrable Heisenberg chain with spin 1. (in Russian), Sov. J. Nucl. Phys. 32

1980

Earlier work this paper cites.

L. A. Takhtajan, The picture of low-lying excitations in the isotropic Heisenberg chain of arbitrary spins, Phys. Lett. A87

1982

Earlier work this paper cites.

H. M. Babujian, Exact solution of the one-dimensional isotropic Heisenberg chain with arbitrary spins S, Phys. Lett. A90

1982

Earlier work this paper cites.

K. Sogo, Ground state and low-lying excitations in the Heisenberg XXZ chain of arbitrary spin S, Phys. Lett. A104

1984

Earlier work this paper cites.

I. Affleck, Exact critical exponents for quantum spin chains, non-linear σ \sigma -models at θ = π \theta=\pi and the quantum Hall effect, Nucl. Phys. B265

1986

Earlier work this paper cites.

I. Affleck, Universal term in the free energy at a critical point and the conformal anomaly, Phys. Rev. Lett. 56

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.

I. Affleck and F. D. M. Haldane, Critical theory of quantum spin chains, Phys. Rev. B36

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. B40

1989

Earlier work this paper cites.

M. N. Barber and M. T. Batchelor, Spectrum of the biquadratic spin-1 antiferromagnetic chain, Phys. Rev. B40

1989

Earlier work this paper cites.

A. Klümper, New results for q-state vertex models and the pure biquadratic spin-1 Hamiltonian, EPL (Europhysics Letters) 9

1989

Earlier work this paper cites.

M. T. Batchelor, L. Mezincescu, R. I. Nepomechie, and V. Rittenberg, q-deformations of the O ⁡ ( 3 ) O(3) symmetric spin-1 Heisenberg chain, J. Phys. A23

1990

Earlier work this paper cites.

M. T. Batchelor, U q ​ [ S ​ U ​ ( 2 ) ] U_{q}[SU(2)] -Invariant Spin Chains, Related Algebras and Finite-Size Corrections, Prog. Theor. Phys. Supp. 102

1990

Earlier work this paper cites.

M. Kashiwara, Crystalizing the q-analogue of universal enveloping algebras, Comm. Math. Phys. 133

1990

Earlier work this paper cites.

G. Lusztig, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3

1990

Earlier work this paper cites.

V. Pasquier and H. Saleur, Common structures between finite systems and conformal field theories through quantum groups, Nucl. Phys. B330

1990

Earlier work this paper cites.

A. Klümper, A. Schadschneider, and J. Zittartz, Equivalence and solution of anisotropic spin-1 models and generalized t-J fermion models in one dimension, J. Phys. A24

1991

Earlier work this paper cites.

A. Klümper, A. Schadschneider, and J. Zittartz, Groundstate properties of a generalized VBS-model, Zeit. Phys. B87

1992

Earlier work this paper cites.

S.-J. Kang, M. Kashiwara, K. C. Misra, T. Miwa, T. Nakashima, and A. Nakayashiki, Affine crystals and vertex models, Int. J. Mod. Phys. A7

1992

Earlier work this paper cites.

A. Klümper, A. Schadschneider, and J. Zittartz, Matrix product ground states for one-dimensional spin-1 quantum antiferromagnets, Europhysics Letters 24

1993

Cited alongside, same era.

Y. Xian, Exact results of dimerization order parameter in SU(n) antiferromagnetic chains, Phys. Lett. A183

1993

Cited alongside, same era.

B. Davies, O. Foda, M. Jimbo, T. Miwa, and A. Nakayashiki, Diagonalization of the XXZ Hamiltonian by vertex operators, Comm. Math. Phys. 151

1993

Cited alongside, same era.

D. Bernard, M. Gaudin, F. D. M. Haldane, and V. Pasquier, Yang-Baxter equation in long-range interacting systems, J. Phys. A26

1993

Cited alongside, same era.

M. T. Batchelor and C. M. Yung, q q -deformations of quantum spin chains with exact valence-bond ground states, Int. J. Mod. Phys. B8

1994

Cited alongside, same era.

F. Pollmann, S. Mukerjee, A. M. Turner, and J. E. Moore, Theory of finite-entanglement scaling at one-dimensional quantum critical points, Phys. Rev. Lett. 102

Original

2009

Later among the works it cites.

H.-H. Tu, G.-M. Zhang, T. Xiang, Z.-X. Liu, and T.-K. Ng, Topologically distinct classes of valence-bond solid states with their parent Hamiltonians, Phys. Rev. B80

Original

2009

Later among the works it cites.

X. Chen, Z.-C. Gu, and X.-G. Wen, Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order, Phys. Rev. B82

Original

2010

Later among the works it cites.

F. Pollmann, A. M. Turner, E. Berg, and M. Oshikawa, Entanglement spectrum of a topological phase in one dimension, Phys. Rev. B81

Original

2010

Later among the works it cites.