Algebraic solution of the Hubbard model on the infinite interval

Abstract

We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite line at zero density. This enables us to diagonalize the Hamiltonian algebraically. The eigenstates can be classified as scattering states of particles, bound pairs of particles and bound states of pairs. We obtain the corresponding creation and annihilation operators and calculate the S-matrix. The Hamiltonian on the infinite line is invariant under the Yangian quantum group Y(su(2)). We show that the n-particle scattering states transform like n-fold tensor products of fundamental representations of Y(su(2)) and that the bound states are Yangian singlet. ‡

Thermodynamics and excitations of the one-dimensional Hubbard model

“…The S-matrix at half-filling [29], on the other hand, possesses the difference property and can therefore be associated with a Y(su(2))⊕Y(su (2)) Yangian [47]. The precise relation between R-matrix and S-matrix is only understood in the rather simple situation of an empty band [48,49]. Because of the lack of the difference property we can neither find a boost operator for the Hubbard model by the reasoning of [93] nor can we associate a spectral curve with it.…”

“…For this reason there are too many candidates for creation and annihilation operators in the algebraic Bethe ansatz [42,44,45]. Again this redundancy has only been partially understood in the empty band case [49]. The known algebraic Bethe ansatz [44,45] is of involved structure and hopefully will be simplified in the future.…”

“…The Hamiltonian is invariant under the direct sum of two Y(su(2)) Yangians [47]. The relation of these Yangians to Shastry's R-matrix was clarified in [48,49], where it was also shown that the eigenstates of the Hubbard Hamiltonian on the infinite interval, at zero density transform like irreducible representations of one of the Yangians.…”

Quantum integrability of bosonic massive Thirring model in continuum

“…14 The quantized version of this DNLS model also preserves the integrability property. 17 In this paper our aim is to establish the integrability property of the quantum BMT model and to obtain the spectrum of all conserved quantities including the Hamiltonian by using the QISM at an infinite interval limit. 14,15 In an earlier work by Kulish and Sklyanin, 6 the Lax operator and the corresponding R-matrix for the quantum BMT model has been given, though the detailed calculations are not being explicitly shown.…”

Conservation laws in the one-dimensional Hubbard model

“…[9][10][11][12] The invariance of the model under two Y͓su͑2͔͒ Yangians was also studied. 13,14 As an alternative to the coordinate Bethe ansatz, the solution of many integrable quantum models can also be obtained by means of the inverse scattering method, first introduced in Ref. 15.…”