scholarly journals Resolution of theGL(3) ⊃O(3) state labelling problem via theO(3)-invariant Bethe subalgebra of the twisted Yangian

2005 ◽  
Vol 38 (14) ◽  
pp. L219-L226 ◽  
Author(s):  
P D Jarvis ◽  
R B Zhang
Keyword(s):  
Twisted Yangian ◽  
Bethe Subalgebra

scholarly journals Spin chain overlaps and the twisted Yangian

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Marius de Leeuw ◽  
Tamás Gombor ◽  
Charlotte Kristjansen ◽  
Georgios Linardopoulos ◽  
Balázs Pozsgay
Keyword(s):  
Spin Chain ◽  
Twisted Yangian

scholarly journals A novel class of translationally invariant spin chains with long-range interactions

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
B. Basu-Mallick ◽  
F. Finkel ◽  
A. González-López
Keyword(s):  
Long Range ◽  
Degrees Of Freedom ◽  
Spin Chains ◽  
Open Chain ◽  
New Class ◽  
Spin Interactions ◽  
Long Range Interactions ◽  
Spin Reversal ◽  
Twisted Yangian ◽  
Internal Degrees Of Freedom

Abstract We introduce a new class of open, translationally invariant spin chains with long-range interactions depending on both spin permutation and (polarized) spin reversal operators, which includes the Haldane-Shastry chain as a particular degenerate case. The new class is characterized by the fact that the Hamiltonian is invariant under “twisted” translations, combining an ordinary translation with a spin flip at one end of the chain. It includes a remarkable model with elliptic spin-spin interactions, smoothly interpolating between the XXX Heisenberg model with anti-periodic boundary conditions and a new open chain with sites uniformly spaced on a half-circle and interactions inversely proportional to the square of the distance between the spins. We are able to compute in closed form the partition function of the latter chain, thereby obtaining a complete description of its spectrum in terms of a pair of independent su(1|1) and su(m/2) motifs when the number m of internal degrees of freedom is even. This implies that the even m model is invariant under the direct sum of the Yangians Y (gl(1|1)) and Y (gl(0|m/2)). We also analyze several statistical properties of the new chain’s spectrum. In particular, we show that it is highly degenerate, which strongly suggests the existence of an underlying (twisted) Yangian symmetry also for odd m.

scholarly journals Principal Realization of Twisted Yangian $${Y(\mathfrak{g}_{N})}$$

2012 ◽  
Vol 102 (1) ◽  
pp. 91-105 ◽  
Author(s):  
Naihuan Jing ◽  
Ming Liu
Keyword(s):  
Twisted Yangian

scholarly journals KZ equations and Bethe subalgebras in generalized Yangians related to compatible $R$-matrices

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Dimitri Gurevich ◽  
Pavel Saponov ◽  
Dmitry Talalaev
Keyword(s):  
Symmetric Polynomials ◽  
Reflection Equation ◽  
Matrix Algebras ◽  
Commutative Subalgebras ◽  
Quantum Matrix ◽  
Zamolodchikov Equation ◽  
Bethe Subalgebra

Abstract The notion of compatible braidings was introduced in Isaev et al. (1999, J. Phys. A, 32, L115–L121). On the base of this notion, the authors of Isaev et al. (1999, J. Phys. A, 32, L115–L121) defined certain quantum matrix algebras generalizing the RTT algebras and Reflection Equation ones. They also defined analogues of some symmetric polynomials in these algebras and showed that these polynomials generate commutative subalgebras, called Bethe. By using a similar approach, we introduce certain new algebras called generalized Yangians and define analogues of some symmetric polynomials in these algebras. We claim that they commute with each other and thus generate a commutative Bethe subalgebra in each generalized Yangian. Besides, we define some analogues (also arising from couples of compatible braidings) of the Knizhnik–Zamolodchikov equation—classical and quantum. Communicated by: Alexander Veselov

scholarly journals Achiral boundaries and the twisted Yangian of the D5-brane

2011 ◽  
Vol 2011 (8) ◽  
Author(s):  
Niall MacKay ◽  
Vidas Regelskis
Keyword(s):  
Twisted Yangian

scholarly journals Nested Algebraic Bethe Ansatz for Open Spin Chains with Even Twisted Yangian Symmetry

2018 ◽  
Vol 20 (2) ◽  
pp. 339-392 ◽  
Author(s):  
Allan Gerrard ◽  
Niall MacKay ◽  
Vidas Regelskis
Keyword(s):  
Bethe Ansatz ◽  
Spin Chains ◽  
Algebraic Bethe Ansatz ◽  
Twisted Yangian ◽  
Yangian Symmetry

scholarly journals Twisted Yangian symmetry of the open Hubbard model

2014 ◽  
Vol 47 (30) ◽  
pp. 305203 ◽  
Author(s):  
Alejandro De La Rosa Gomez ◽  
Niall J MacKay
Keyword(s):  
Hubbard Model ◽  
Twisted Yangian ◽  
Yangian Symmetry
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