Inhomogeneous quantum groups are shown to be an effective algebraic tool in the study of integrable systems. The method is illustrated on the one-dimensional Heisenberg ferromagnet whose symmetry is investigated by means of the quantum Galilei group ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{q}}$(1) here introduced. Both the single magnon and the s=1/2 bound states of n magnons are completely described by the algebra. Therefore, some of the results provided by the Bethe-ansatz method emerge as a natural consequence of the quantum symmetry of the discrete chain.Inhomogeneous quantum groups are shown to be an effective algebraic tool in the study of integrable systems. The method is illustrated on the one-dimensional Heisenberg ferromagnet whose symmetry is investigated by means of the quantum Galilei group ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{q}}$(1) here introduced. Both the single magnon and the s=1/2 bound states of n magnons are completely described by the algebra. Therefore, some of the results provided by the Bethe-ansatz method emerge as a natural consequence of the quantum symmetry of the discrete chain.

arXiv:hep-th/9203048Physical review. B, Condensed matterSep 1, 199236 citations

Group Actions and Classification of Quantum States of the Heisenberg Model of Magnetism

Tadeusz Lulek

Springer eBooksJan 1, 20010 citations

Heisenberg XXZ model and quantum Galilei group

F Bonechi, E Celeghini, R Giachetti +2 more

The 1D Heisenberg spin model with an anisotropy of the XXZ type is analysed in terms of the symmetry given by the quantum Galilei group Gamma q (1). For a chain with an infinite number of sites the authors show that the magnon excitations and the s=1/2, n-magnon bound states are determined by the algebra. In this case the Gamma q (1) symmetry provides a description naturally compatible with the Bethe ansatz. The recurrence relations determined by Gamma q (1) permit one to express the energy of the n-magnon bound states in a closed form in terms of Tchebischeff polynomials.The 1D Heisenberg spin model with an anisotropy of the XXZ type is analysed in terms of the symmetry given by the quantum Galilei group Gamma q (1). For a chain with an infinite number of sites the authors show that the magnon excitations and the s=1/2, n-magnon bound states are determined by the algebra. In this case the Gamma q (1) symmetry provides a description naturally compatible with the Bethe ansatz. The recurrence relations determined by Gamma q (1) permit one to express the energy of the n-magnon bound states in a closed form in terms of Tchebischeff polynomials.

arXiv:hep-th/9204054Journal of Physics A Mathematical and GeneralAug 7, 199246 citations

Renormalization group analysis for bosonization coefficients in half-odd-integer Kitaev spin chains

Jianxun Li, Chao Xu, Wang Yang

Based on a renormalization-group (RG) analysis, we study the bosonization formulas for spin- $S$ Kitaev-Gamma and Kitaev-Heisenberg-Gamma chains in the parameter regime $K<0$ , $Γ>0$ , and $J>0$ , with $S$ being a half-odd integer. We find that the effects associated with the breaking of emergent continuous symmetries in the bosonization formulas scale as $1/S$ in the large- $S$ limit, in qualitative agreement with density-matrix renormalization-group (DMRG) results for Kitaev-Gamma chains. For Kitaev-Heisenberg-Gamma chains, the low-energy excitations are characterized by incommensurate gapless wave vectors, and symmetry analysis yields ten independent bosonization coefficients, five of which are predicted by the RG analysis to be independent of the Heisenberg coupling up to linear order. Our results provide useful input for determining magnetic ordering tendencies in two-dimensional Kitaev spin models within a quasi-one-dimensional approach.Based on a renormalization-group (RG) analysis, we study the bosonization formulas for spin-$S$ Kitaev-Gamma and Kitaev-Heisenberg-Gamma chains in the parameter regime $K<0$, $Γ>0$, and $J>0$, with $S$ being a half-odd integer. We find that the effects associated with the breaking of emergent continuous symmetries in the bosonization formulas scale as $1/S$ in the large-$S$ limit, in qualitative agreement with density-matrix renormalization-group (DMRG) results for Kitaev-Gamma chains. For Kitaev-Heisenberg-Gamma chains, the low-energy excitations are characterized by incommensurate gapless wave vectors, and symmetry analysis yields ten independent bosonization coefficients, five of which are predicted by the RG analysis to be independent of the Heisenberg coupling up to linear order. Our results provide useful input for determining magnetic ordering tendencies in two-dimensional Kitaev spin models within a quasi-one-dimensional approach.

arXiv:2605.03582Physical review. B./Physical review. BSep 21, 20260 citations

Based on a renormalization-group (RG) analysis, we study the bosonization formulas for spin-

S

Kitaev-Gamma and Kitaev-Heisenberg-Gamma chains in the parameter regime

K<0

Γ>0

, and

J>0

, with

S

being a half-odd integer. We find that the effects associated with the breaking of emergent continuous symmetries in the bosonization formulas scale as

1/S

in the large-

S

limit, in qualitative agreement with density-matrix renormalization-group (DMRG) results for Kitaev-Gamma chains. For Kitaev-Heisenberg-Gamma chains, the low-energy excitations are characterized by incommensurate gapless wave vectors, and symmetry analysis yields ten independent bosonization coefficients, five of which are predicted by the RG analysis to be independent of the Heisenberg coupling up to linear order. Our results provide useful input for determining magnetic ordering tendencies in two-dimensional Kitaev spin models within a quasi-one-dimensional approach.