The Yangian Symmetry of the Hubbard Models with Variable Range Hopping

Abstract

We present two pairs of Y($s{l}_2$) Yangian symmetries for the trigonometric and hyperbolic versions of the Hubbard model with non-nearest-neighbour hopping. In both cases the Yangians are mutually commuting, hence can be combined into a Y($s{l}_2$)$\oplus$Y($s{l}_2$) Yangian. Their mutual commutativity is of dynamical origin. The known Yangians of the Haldane-Shastry spin chain and the nearest neighbour Hubbard model are contained as limiting cases of our new representations.

10 pages, Latex

References in corpus (6)

• Correlation Functions of the XXZ model for $\Delta <-1$
• Yang-Baxter equation in spin chains with long range interactions
• An Introduction to Yangian Symmetries
• The Yangian symmetry of the Hubbard Model
• Integrals of motion of the Haldane Shastry Model
• Charge and Spin Gap Formation in Exactly Solvable Hubbard Chains with Long-Rang Hopping

Cited by in corpus (14)

• Fermionic representations of integrable lattice systems
• Yangian Symmetry and Quantum Inverse Scattering Method for the One-Dimensional Hubbard Model
• Algebraic Solution of the Hubbard Model on the Infinite Interval
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Exactly integrable family of generalized Hubbard models with twisted Yangian symmetry
• Yangian description for decays and possible explanation of $X$ in the decay $K_L^0\to {\pi }^0{\pi }^{0}X$
• Many-spinon states and representations of Yangians in the SU(n) Haldane--Shastry model
• New integrable extension of the Hubbard chain with variable range hopping
• How to fold a spin chain: Integrable boundaries of the Heisenberg XXX and Inozemtsev hyperbolic models
• The particle-hole transformation, supersymmetry and achiral boundaries of the open Hubbard model
• A solvable non-unitary fermionic long-range model with extended symmetry
• Scalar Symmetries of the Hubbard Models with Variable Range Hopping
• Twisted Yangian symmetry of the open Hubbard model
• Y(so(5)) symmtry of the nonlinear Schr$\ddot{o}$dinger model with four-cmponents