Abstract We argue that the Hamiltonians for A 2 n ( 2 ) open quantum spin chains corresponding to two choices of integrable boundary conditions have the symmetries U q ( B n ) and U q ( C n ) , respectively. We find a formula for the Dynkin labels of the Bethe states (which determine the degeneracies of the corresponding eigenvalues) in terms of the numbers of Bethe roots of each type. With the help of this formula, we verify numerically (for a generic value of the anisotropy parameter) that the degeneracies and multiplicities of the spectra implied by the quantum group symmetries are completely described by the Bethe ansatz.Abstract We argue that the Hamiltonians for A 2 n ( 2 ) open quantum spin chains corresponding to two choices of integrable boundary conditions have the symmetries U q ( B n ) and U q ( C n ) , respectively. We find a formula for the Dynkin labels of the Bethe states (which determine the degeneracies of the corresponding eigenvalues) in terms of the numbers of Bethe roots of each type. With the help of this formula, we verify numerically (for a generic value of the anisotropy parameter) that the degeneracies and multiplicities of the spectra implied by the quantum group symmetries are completely described by the Bethe ansatz.

arXiv:1702.01482Journal of Physics A Mathematical and TheoreticalMay 31, 20175 citations

Chaos in systems with quantum group symmetry

Victor Gorbenko, A.N. Zhabin

Quantum groups have a long and fruitful history of applications in integrable systems. Can quantum group symmetries exist in the absence of integrability? We provide an explicit example of a system with quantum group global symmetry which is chaotic. The example is a spin chain with next-to-nearest interaction term. We show the chaotic behavior of the system by studying the Eigenvalue statistics. The spin chain is non-unitary but PT-symmetric and, in addition to chaos, exhibits an interesting transition after which the eigenvalues become complex.Quantum groups have a long and fruitful history of applications in integrable systems. Can quantum group symmetries exist in the absence of integrability? We provide an explicit example of a system with quantum group global symmetry which is chaotic. The example is a spin chain with next-to-nearest interaction term. We show the chaotic behavior of the system by studying the Eigenvalue statistics. The spin chain is non-unitary but PT-symmetric and, in addition to chaos, exhibits an interesting transition after which the eigenvalues become complex.

arXiv:2510.23247Physical review. B./Physical review. BJul 27, 20260 citations

Interacting quantum spin chains

A. Zheludev

Applied Physics ADec 1, 200211 citations

Quantum Spin Chains

Jill C. Bonner, Henk W. J. Blöte, Hans Beck +1 more

Springer series in solid-state sciencesJan 1, 198146 citations

Classification of symmetry protected states of quantum spin chains for continuous symmetry groups

Bruno de O. Carvalho, Wojciech De Roeck, Tijl Jappens

Symmetry protected states (SPT's) of quantum spin systems were studied by several authors. For one-dimensional systems (spin chains), there is an essentially complete and rigorous understanding: SPT's corresponding to finite on-site symmetry groups $G$ are classified by the second cohomology group $H^2(G,U(1))$ , as established by Kapustin et al. [J. Math. Phys. (2021)]. We extend this result to the case of compact topological symmetry groups $G$ . We also strengthen the existing results in the sense that our classification results holds within the class of spin chains with locally bounded on-site dimensions.Symmetry protected states (SPT's) of quantum spin systems were studied by several authors. For one-dimensional systems (spin chains), there is an essentially complete and rigorous understanding: SPT's corresponding to finite on-site symmetry groups $G$ are classified by the second cohomology group $H^2(G,U(1))$, as established by Kapustin et al. [J. Math. Phys. (2021)]. We extend this result to the case of compact topological symmetry groups $G$. We also strengthen the existing results in the sense that our classification results holds within the class of spin chains with locally bounded on-site dimensions.

arXiv:2409.01112Sep 2, 20240 citations

G

are classified by the second cohomology group

H^2(G,U(1))

, as established by Kapustin et al. [J. Math. Phys. (2021)]. We extend this result to the case of compact topological symmetry groups

G

. We also strengthen the existing results in the sense that our classification results holds within the class of spin chains with locally bounded on-site dimensions.