The Yangian symmetry of the Hubbard Model

Abstract

We discovered new hidden symmetry of the one-dimensional Hubbard model. We showthat the one-dimensional Hubbard model on the infinite chain has the infinite-dimensional algebra of symmetries. This algebra is a direct sum of two $sl(2)$-Yangians. This $Y(sl(2))\oplus Y(sl(2))$ symmetry is an extension of the well-known $sl(2)\oplus sl(2)$ . The deformation parameters of the Yangians are equal up to the signs to the coupling constant of the Hubbard model hamiltonian.

7 pages, ITP-SB-93-66

References in corpus (6)

• Correlation Functions of the XXZ model for $\Delta <-1$
• Yang-Baxter equation in spin chains with long range interactions
• Diagonalization of the XXZ Hamiltonian by Vertex Operators
• Quantum affine symmetry in vertex models
• Scattering Matrix and Excitation Spectrum of the Hubbard Model
• Supersymmetry and the Nonlocal Yangian Deformation Symmetry

Cited by in corpus (50)

• Introduction to Yangian symmetry in integrable field theory
• Quantum Deformations of the One-Dimensional Hubbard Model
• Superdiffusion in spin chains
• Matrix product solutions of boundary driven quantum chains
• The Quantum Inverse Scattering Method for Hubbard-like Models
• The Hubbard chain at finite temperatures: ab initio calculations of Tomonaga-Luttinger liquid properties
• Algebraic Bethe ansatz approach for the one-dimensional Hubbard model
• Finite-dimensional irreducible representations of twisted Yangians
• Lower bounds on high-temperature diffusion constants from quadratically extensive almost conserved operators
• Yang-Baxter and the Boost: splitting the difference
• The Yangian Symmetry of the Hubbard Models with Variable Range Hopping
• Fermionic representations of integrable lattice systems
• A method to efficiently simulate the thermodynamical properties of the Fermi-Hubbard model on a quantum computer
• Yangian Symmetry and Quantum Inverse Scattering Method for the One-Dimensional Hubbard Model
• Infinitely dimensional Lax structure for one-dimensional Hubbard model
• Fermionic R-Operator and Integrability of the One-Dimensional Hubbard Model
• Algebraic approach in unifying quantum integrable models
• The RTT-Realization for the Deformed gl(2|2) Yangian
• The Bound State S-matrix of the Deformed Hubbard Chain
• Pseudoparticle approach to 1D integrable quantum models
• Algebraic Solution of the Hubbard Model on the Infinite Interval
• Algebraic and Analytic Properties of the One-Dimensional Hubbard Model
• SO(4) Symmetry of the Transfer Matrix for the One-Dimensional Hubbard Model
• Exact solution of the lattice vertex model analog of the coupled Bariev XY chains
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Absence of ballistic charge transport in the half-filled 1D Hubbard model
• Exactly integrable family of generalized Hubbard models with twisted Yangian symmetry
• Representations of centrally extended Lie superalgebra $\mathfrak{psl}(2|2)$
• Maximally extended sl(2|2) as a quantum double
• Yangians and their applications
• Quantum critical behavior and thermodynamics of the repulsive one-dimensional Hubbard model in a magnetic field
• Finite-difference representations of the degenerate affine Hecke algebra
• Symmetries in the Hubbard model with n-fold orbital degeneracy
• Formfactors in the half-filled Hubbard model
• The Yangian of sl(n|m) and the universal R-matrix
• An algebraic approach to the Hubbard model
• 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
• Quantum Symmetry of Hubbard Model Unraveled
• Symmetries of Spin Calogero Models
• The particle-hole transformation, supersymmetry and achiral boundaries of the open Hubbard model
• Drinfeld realization of the centrally extended $\mathfrak{psl}(2|2)$ Yangian algebra with the manifest coproducts
• Supergroup approach to the Hubbard model
• Super-Yangian Y(gl(1|1)) and Its Oscillator Realization
• Quantum Systems Exactly
• The functional integral in the Hubbard model
• Twisted Yangian symmetry of the open Hubbard model
• Y(so(5)) symmtry of the nonlinear Schr$\ddot{o}$dinger model with four-cmponents
• On the Integrable Structure of Super Yang-Mills Scattering Amplitudes