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

Wen, Fakai; Yang, Zhan-Ying; Yang, Tao; Hao, Kun; Cao, Junpeng; Yang, Wen-Li

doi:10.1007/jhep06(2018)076

Cited by 8 publications

(14 citation statements)

References 45 publications

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“…So far many attempts have been done to solve the resulting BAEs from inhomogeneous T − Q relations [17][18][19][20][21][22], the corresponding distribution of Bethe roots for ground-state or elementary excitation states is still an interesting open problem [12]. Here we propose a way to study the thermodynamic limit of the spin- 1 2 XYZ chain with an antiperiodic boundary condition, which was successfully applied to the XXZ spin chain with open boundary conditions [18].…”

Section: Jhep12(2020)146mentioning

confidence: 99%

Thermodynamic limit of the spin-$$ \frac{1}{2} $$ XYZ spin chain with the antiperiodic boundary condition

Xin

Cao

et al. 2020

J. High Energ. Phys.

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Based on its off-diagonal Bethe ansatz solution, we study the thermodynamic limit of the spin-$$ \frac{1}{2} $$ 1 2 XYZ spin chain with the antiperiodic boundary condition. The key point of our method is that there exist some degenerate points of the crossing parameter ηm,l, at which the associated inhomogeneous T − Q relation becomes a homogeneous one. This makes extrapolating the formulae deriving from the homogeneous one to an arbitrary η with O(N−2) corrections for a large N possible. The ground state energy and elementary excitations of the system are obtained. By taking the trigonometric limit, we also give the results of antiperiodic XXZ spin chain within the gapless region in the thermodynamic limit, which does not have any degenerate points.

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Section: Jhep12(2020)146mentioning

confidence: 99%

Thermodynamic limit of the spin-$$ \frac{1}{2} $$ XYZ spin chain with the antiperiodic boundary condition

Xin

Cao

et al. 2020

J. High Energ. Phys.

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“…where σ ′ (u) = ∂ ∂u σ(u). Although many attempts have been done to solve the resulting BAEs from inhomogeneous T − Q relations [17][18][19][20][21][22], the corresponding distributions of Bethe roots for ground-state or elementary excitation states is still an interesting open problem. This motivates us in this paper to look for another way, instead of solving the BAEs (2.13) for a large N, to study the thermodynamic limit of the spin- 1 2 XYZ chain with the antiperiodic boundary condition.…”

Section: Antiperiodic Xyz Model and Its Exact Solutionsmentioning

confidence: 99%

“…So far many attempts have been done to solve the resulting BAEs from inhomogeneous T − Q relations [17][18][19][20][21][22], the corresponding distribution of Bethe roots for ground-state or elementary excitation states is still an interesting open problem [12]. Here we propose a way to study the thermodynamic limit of the spin- 1 2 XYZ chain with an antiperiodic boundary condition, which was succeeded in applying to the XXZ spin chain with open boundary conditions [18].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic limit and twisted boundary energy of the XXZ spin chain with antiperiodic boundary condition

et al. 2018

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We investigate the thermodynamic limit of the inhomogeneous T − Q relation of the antiferromagnetic XXZ spin chain with antiperiodic boundary condition. It is shown that the contribution of the inhomogeneous term for the ground state can be neglected when the system-size N tends to infinity, which enables us to reduce the inhomogeneous Bethe ansatz equations (BAEs) to the homogeneous ones. Then the quantum numbers at the ground states are obtained, by which the system with arbitrary size can be studied. We also calculate the twisted boundary energy of the system. the contribution of the inhomogeneous term with finite system-size N . We find that the contribution of the inhomogeneous term in the associated T − Q relation to the ground state energy can be neglected when the system-size N tends to infinity. Because we consider the massive region of the system, the ground state energy with even N and that with odd N are different. The value of energy difference is proportional to the energy of one bond. We also check our results by using the density matrix renormalization group (DMRG) method [23,24], which leads to that the numerical results and the analytic one are consistent with each other very well. As a consequence, we obtain the twisted boundary energy of the model. The paper is organized as follows. In the next section, the model and the associated ODBA solutions are introduced. In section 3, we study the finite-size effects of contribution of the inhomogeneous term in the T − Q relation for the ground state. The thermodynamic limit of the XXZ spin chain with antiperiodic and with periodic boundary conditions are discussed in section 4 and section 5, respectively. The twisted boundary energy is given in Section 6. Section 7 is the concluding remarks and discussions. Some supporting detailed calculations are given in Appendices A&B.

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“…The patterns of roots of inhomogeneous Bethe ansatz equations are very complicated. Only for some special cases, the distribution of roots of the degenerate Bethe ansatz equations are found and the related physical properties are studied 34 .…”

Section: Introductionmentioning

confidence: 99%

Surface energy of the one-dimensional supersymmetric $t-J$ model with general integrable boundary terms in the antiferromagnetic sector

Sun,

Chen,

Yang

et al. 2021

Preprint

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In this paper, we study the surface energy of the one-dimensional supersymmetric t−J model with unparallel boundary magnetic fields, which is a typical U (1)-symmetry broken quantum integrable strongly correlated electron system. It is shown that at the ground state, the contribution of inhomogeneous term in the Bethe ansatz solution of eigenvalues of transfer matrix satisfies the finite size scaling law L β where β < 0. Based on it, the physical quantities of the system in the thermodynamic limit are calculated. We obtain the patterns of Bethe roots and the analytical expressions of density of states, ground state energy and surface energy. We also find that there exist the stable boundary bound states if the boundary fields satisfy some constraints.

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

Cited by 8 publications

References 45 publications

Thermodynamic limit of the spin-$$ \frac{1}{2} $$ XYZ spin chain with the antiperiodic boundary condition

Thermodynamic limit of the spin-$$ \frac{1}{2} $$ XYZ spin chain with the antiperiodic boundary condition

Thermodynamic limit and twisted boundary energy of the XXZ spin chain with antiperiodic boundary condition

Surface energy of the one-dimensional supersymmetric $t-J$ model with general integrable boundary terms in the antiferromagnetic sector

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