Yangian and Topological Basis Expressions of Two Types of XXZ Spin Chains

Du, Guijiao; Xue, Kang; Zhou, Chengcheng

doi:10.1007/s10773-019-04107-6

Yangian and Topological Basis Expressions of Two Types of XXZ Spin Chains

May 4, 2019

17 pages

Published in:

Int.J.Theor.Phys. 58 (2019) 7, 2167-2183

Published: May 4, 2019

DOI:

10.1007/s10773-019-04107-6

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AMS MathSciNet

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Abstract: (Springer)

We construct a set of orthogonal topological basis states, based on which Temperley-Lieb algebra (TLA) generators U

_{ij}

can be reduced into four subspaces. According to the relations between the XXZ model and TLA generators U

_{ij}

, two types of eigenstates of the XXZ model can be expressed by a topological basis. We also analyze the Yangian realizations of XXZ model systems and illustrate them with figures.

Topological basis
Yangian
Spin model

References(21)

Figures(0)

[1]

Hopf algebras and the quantum Yang-Baxter equation

V.G. Drinfeld
(
- Kharkov, Inst. Low Temp. Phys.
)

- Sov.Math.Dokl. 32 (1985) 254-258,
- Dokl.Akad.Nauk Ser.Fiz. 283 (1985) 1060-1064

[2]

A New realization of Yangians and quantized affine algebras

V.G. Drinfeld

- Sov.Math.Dokl. 36 (1988) 212-216

[3]

Yangians and classical Lie algebras

Alexander Molev
(
- Australian Natl. U., Canberra
)
,
Maxim Nazarov
(
- Swansea U.
)
,
Grigori Olshansky
(
- IITP, Moscow
)

- Russ.Math.Surveys 51 (1996) 205
•
e-Print:
- hep-th/9409025
•
DOI:
- 10.1070/RM1996v051n02ABEH002772

[4]

Ge, M.-L., Jing, N

C.-M. Bai

- J.Math.Phys. 50 (2009) 013518
•
DOI:
- 10.1063/1.3050319

[5]

: Yangians and their applications. ScienceDirect 3(03), 907-959

A.I. Molev

[6]

: Quantum groups. In: Proc. int. congress math., pp. 798-820. AMS, Berkeley

V.G. Drinfeld

[7]

: Quantum spectral transform method: recent developments. In: Integrable quantum field theories, lecture notes in phys, vol. 151, pp. 61-119

P.P. Kulish
,
E.K. Sklyanin

[8]

: Quantum inverse scattering method and the Heisenberg XYZ-model. Russian Math. Surv. 34(5), 11-68

L.A. Takhtajan
,
L.D. Faddeev

•
DOI:
- 10.1070/RM1979v034n05ABEH003909

[9]

A Direct calculation of the spectrum of masses in an integrable model from the Hopf algebra symmetry

A.A. Belavin
(
- Moscow, ITEP
)

- Phys.Lett.B 283 (1992) 67-69
•
DOI:
- 10.1016/0370-2693(92)91428-C

[10]

Introduction to Yangian symmetry in integrable field theory

N.J. MacKay
(
- York U., England, Dept. Math.
)

- Int.J.Mod.Phys.A 20 (2005) 7189-7218
•
e-Print:
- hep-th/0409183
•
DOI:
- 10.1142/S0217751X05022317

[11]

Yangian symmetry of integrable quantum chains with long range interactions and a new description of states in conformal field theory

F.D.M. Haldane
(
- Princeton U. and
- Ecole Normale Superieure
)
,
Z.N.C. Ha
(
- Princeton U. and
- Ecole Normale Superieure
)
,
J.C. Talstra
(
- Princeton U. and
- Ecole Normale Superieure
)
,
Denis Bernard
(
- Saclay
)
,
V. Pasquier
(
- Saclay
)

- Phys.Rev.Lett. 69 (1992) 2021-2025
•
DOI:
- 10.1103/PhysRevLett.69.2021

[12]

:

S. Murakami
,
F. Göhmann

- Phys.Lett.A 227 (1997) 216-226
•
DOI:
- 10.1016/S0375-9601(96)00953-X

[13]

The Yangian symmetry of the Hubbard model

D.B. Uglov
(
- SUNY, Stony Brook
)
,
V.E. Korepin
(
- SUNY, Stony Brook
)

- Phys.Lett.A 190 (1994) 238-242,
•
e-Print:
- hep-th/9310158
•
DOI:
- 10.1016/0375-9601(94)90748-X

[14]

The Yangian symmetry of the Hubbard models with variable range hopping

Frank Gohmann
(
- Tokyo U.
)
,
Vladimir Inozemtsev
(
- Tokyo U., ISSP
)

- Phys.Lett.A 214 (1996) 161
•
e-Print:
- cond-mat/9512071
•
DOI:
- 10.1016/0375-9601(96)00174-0

[15]

Ha, Z.N

F.D. Haldane

- J.Phys.Condens.Matter 47 (1993) 12459
•
DOI:
- 10.1103/PhysRevB.47.12459

[16]

: Integrable quantum field theories

P.P. Kulish
,
E.K. Slyanin

- Lect.Notes Phys. 151 (1982) 61C

[17]

Ge, M.L., Xue, K., Zhang, H.B

C.M. Bai

[18]

: Review of Mordern

C. Nayak
,
S.H. Simon
,
A. Stern
,
M. Freedman
,
S.D. Sarma

- Physics 80 (2007) 1083-1159

[19]

Hu, S.W

K. Xue

- Phys.Rev.A 78 (2008) 022319
•
DOI:
- 10.1103/PhysRevA.78.022319

[20]

Relations between the 'percolation' and 'colouring' problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the 'percolation' problem

H.N.V. Temperley
(
- Swansea U.
)
,
E.H. Lieb
(
- Swansea U.
)

- Proc.Roy.Soc.Lond.A 322 (1971) 251-280
•
DOI:
- 10.1098/rspa.1971.0067

[21]

: Yang-Baxter equations on integrable systems

M. Jimbo

•
DOI:
- 10.1142/1021