Spectrum of the supersymmetric model with non-diagonal open boundaries

Abstract

In this work we diagonalize the double-row transfer matrix of the supersymmetric t-J model with non-diagonal boundary terms by means of the algebraic Bethe ansatz. The corresponding reflection equations are studied and two distinct classes of solutions are found, one diagonal solution and other non-diagonal. In the non-diagonal case the eigenvalues in the first sectors are given for arbitrary values of the boundary parameters.

Surface energy of the one-dimensional supersymmetric t − J model with unparallel boundary fields

“…E true is the energy of Hamiltonian (1.1), which can be obtained by using the density matrix renormalization group (DMRG) [36]. For the ground state, the number of Bethe roots reduces to M = L/2 andM = 0, 10) where I j ∈ {1, 2, · · · , L/2}, ζ = 1/2 − ξ ′ and ζ ≥ 0. Then "ground state energy" E hom is given by equation (3.6) with the constraint (3.10).…”

“…In general, the Hamiltonian includes nearest-neighbor hopping (t) and nearest-neighbor spin exchange and charge interactions (J) (see below (1.1)) for the periodic case [8]. For the open case, the Hamiltonian also includes the boundary chemical potentials χ 1 , χ L and the boundary fields h 1 , h L [9,10] S j · S j+1 − 1 4 n j n j+1…”

On the Bethe states of the one-dimensional supersymmetric t − J model with generic open boundaries

“…It is well-known that the one-dimensional t−J model is integrable at the supersymmetric point J = ±2t [7][8][9], and the model with the periodic boundary condition or the diagonal boundaries has been studied by employing many Bethe ansatz methods [10][11][12][13][14][15][16][17][18][19][20]. For the non-diagonal boundary case, the nested algebraic Bethe ansatz method doesn't work since the U (1) symmetry is broken.…”

On the $$\mathcal{{U}}_{q}[osp(1|2)]$$ U q [ o s p ( 1 | 2 ) ] Temperley–Lieb Model

“…For instance, the diagonal solutions associated with the U q [sl(m|n) [12,13] and U q [osp(2|2)] symmetries [14] and non-diagonal solutions related to super-Yangians osp(m|n) [15] and sl(m|n) [16,17]. The most general set of solutions of the reflection equation for the vertex models based on Lie superalgebras are reported in [18].…”