Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2102.02643 · Physical review. B./Physical review. B

Exact surface energy and helical spinons in the XXZ spin chain with arbitrary nondiagonal boundary fields

Yi Qiao, Junpeng Cao, Wen‐Li Yang, Kangjie Shi, Yupeng Wang

Published Jun 1, 2021• 21 citations
arXivHTMLPDF

Abstract

An analytic method is proposed to compute the surface energy and elementary excitations of the XXZ spin chain with generic nondiagonal boundary fields. For the gapped case, in some boundary parameter regimes the contributions of the two boundary fields to the surface energy are nonadditive. Such a correlation effect between the two boundaries also depends on the parity of the site number $N$ even in the thermodynamic limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$. For the gapless case, contributions of the two boundary fields to the surface energy are additive due to the absence of long-range correlation in the bulk. Although the $U(1)$ symmetry of the system is broken, exact spinonlike excitations, which obviously do not carry spin-$\frac{1}{2}$, are observed. The present method provides a universal procedure to deal with quantum integrable systems either with or without $U(1)$ symmetry.

DOI
10.1103/physrevb.103.l220401

Related papers

Surface energy and elementary excitations of the XYZ spin chain with integrable open boundary fields

Zhirong Xin, Junpeng Cao, Wen‐Li Yang +1 more

A bstract We study the thermodynamic limit of the anisotropic XYZ spin chain with non-diagonal integrable open boundary conditions. Although the U(1)-symmetry is broken, by using the new parametrization scheme, we exactly obtain the surface energy and the excitation energy of the system, which has solved the difficulty in the inhomogeneous T − Q relation. With the boundary parameters in the regions making the Hamiltonian Hermitian, we have obtained the distribution patterns of the zeros of the eigenvalue of the transfer matrix for the ground state and the excited ones. We find that the surface and excitation energies depend on the parities of sites number N , due to the long-range Neel order in the bulk. The easy-axis and thermodynamic limit for all the regions of boundary parameters are studied. We also obtain the physical quantities in the thermodynamic limit of boundary XXZ model by taking the trigonometric limit.

arXiv:2404.19240•Journal of High Energy Physics•Oct 10, 2024•2 citations

Surface energy and elementary excitations of the XXZ spin chain with arbitrary boundary fields

Pei Sun, Zhi-Rong Xin, Yi Qiao +5 more

Abstract The thermodynamic properties of the XXZ spin chain with integrable open boundary conditions at the gaped region (i.e. the anisotropic parameter being a real number) are investigated. It is shown that the contribution of the inhomogeneous term in the T − Q relation of the ground state and elementary excited state can be neglected when the size of the system N tends to infinity. The surface energy and elementary excitations induced by the unparallel boundary magnetic fields are obtained.

arXiv:1901.01514•Journal of Physics A Mathematical and Theoretical•May 17, 2019•12 citations

Exact surface energy and elementary excitations of the XXX spin-1/2 chain with arbitrary non-diagonal boundary fields

Jia-Sheng Dong, Pengcheng Lu, Pei Sun +4 more

We study the physical properties of the XXX spin-1/2 chain with arbitrary non-diagonal boundary fields. By using a combination of numerical analysis and analytical method, we obtain the surface energy and elementary excitations of the model. It shows that the contributions of the two boundary fields to the surface energy are additive. We also find that there exists a kind of excitations related to the boundary string.

Chinese Physics B•Oct 7, 2022•3 citations

Thermodynamic limit and surface energy of the XXZ spin chain with arbitrary boundary fields

Yuanyuan Li, Junpeng Cao, Wen‐Li Yang +2 more

In two previous papers [26], [27], the exact solutions of the spin-12 chains with arbitrary boundary fields were constructed via the off-diagonal Bethe ansatz (ODBA). Here we introduce a method to approach the thermodynamic limit of those models. The key point is that at a sequence of degenerate points of the crossing parameter η=ηm, the off-diagonal Bethe ansatz equations (BAEs) can be reduced to the conventional ones. This allows us to extrapolate the formulae derived from the reduced BAEs to arbitrary η case with O(N−2) corrections in the thermodynamic limit N→∞. As an example, the surface energy of the XXZ spin chain model with arbitrary boundary magnetic fields is derived exactly. This approach can be generalized to all the ODBA solvable models.

arXiv:1401.3045•Nuclear Physics B•Apr 18, 2014•54 citations

Exact solutions and elementary excitations in the XXZ spin chain with unparallel boundary fields

Junpeng Cao, Hai‐Qing Lin, Kangjie Shi +1 more

By using a set of gauge transformations, the exact solutions of the XXZ spin chain with unparallel boundary magnetic fields are derived in the framework of the algebraic Bethe ansatz. In the easy-plane case, we show the elementary excitations are some kind of spinons without definite spin because the U(1) symmetry is broken, while in the easy-axis ferromagnetic case a spiral state is realized in the ground state. The correlation functions, the spin torque as well as the spin voltage for the later case are also derived.

arXiv:cond-mat/0212163•Dec 8, 2002•39 citations

Exact ground state and elementary excitations of a topological spin chain

Yi Qiao, Pei Sun, Junpeng Cao +3 more

A novel Bethe ansatz scheme is proposed to calculate physical properties of quantum integrable systems without $U(1)$ symmetry. As an example, the antiperiodic XXZ spin chain, a typical correlated many-body system embedded in a topological manifold, is examined. Conserved ``momentum'' and ``charge'' operators are constructed despite the absence of translational invariance and $U(1)$ symmetry. The ground state energy and elementary excitations are derived exactly. It is found that two intrinsic fractional (one half) zero modes accounting for the double degeneracy exist in the eigenstates. The elementary excitations show quite a different picture from that of a periodic chain. This method can be applied to other quantum integrable models either with or without $U(1)$ symmetry.

arXiv:2003.07089•Physical review. B./Physical review. B•Aug 7, 2020•20 citations
An analytic method is proposed to compute the surface energy and elementary excitations of the XXZ spin chain with generic nondiagonal boundary fields. For the gapped case, in some boundary parameter regimes the contributions of the two boundary fields to the surface energy are nonadditive. Such a correlation effect between the two boundaries also depends on the parity of the site number NNN even in the thermodynamic limit N\ensuremath→\ensuremath∞N\ensuremath{\rightarrow}\ensuremath{\infty}N\ensuremath→\ensuremath∞. For the gapless case, contributions of the two boundary fields to the surface energy are additive due to the absence of long-range correlation in the bulk. Although the U(1)U(1)U(1) symmetry of the system is broken, exact spinonlike excitations, which obviously do not carry spin-12\frac{1}{2}21​, are observed. The present method provides a universal procedure to deal with quantum integrable systems either with or without U(1)U(1)U(1) symmetry.
A bstract We study the thermodynamic limit of the anisotropic XYZ spin chain with non-diagonal integrable open boundary conditions. Although the U(1)-symmetry is broken, by using the new parametrization scheme, we exactly obtain the surface energy and the excitation energy of the system, which has solved the difficulty in the inhomogeneous T − Q relation. With the boundary parameters in the regions making the Hamiltonian Hermitian, we have obtained the distribution patterns of the zeros of the eigenvalue of the transfer matrix for the ground state and the excited ones. We find that the surface and excitation energies depend on the parities of sites number N , due to the long-range Neel order in the bulk. The easy-axis and thermodynamic limit for all the regions of boundary parameters are studied. We also obtain the physical quantities in the thermodynamic limit of boundary XXZ model by taking the trigonometric limit.
Abstract The thermodynamic properties of the XXZ spin chain with integrable open boundary conditions at the gaped region (i.e. the anisotropic parameter being a real number) are investigated. It is shown that the contribution of the inhomogeneous term in the T − Q relation of the ground state and elementary excited state can be neglected when the size of the system N tends to infinity. The surface energy and elementary excitations induced by the unparallel boundary magnetic fields are obtained.
In two previous papers [26], [27], the exact solutions of the spin-12 chains with arbitrary boundary fields were constructed via the off-diagonal Bethe ansatz (ODBA). Here we introduce a method to approach the thermodynamic limit of those models. The key point is that at a sequence of degenerate points of the crossing parameter η=ηm, the off-diagonal Bethe ansatz equations (BAEs) can be reduced to the conventional ones. This allows us to extrapolate the formulae derived from the reduced BAEs to arbitrary η case with O(N−2) corrections in the thermodynamic limit N→∞. As an example, the surface energy of the XXZ spin chain model with arbitrary boundary magnetic fields is derived exactly. This approach can be generalized to all the ODBA solvable models.
By using a set of gauge transformations, the exact solutions of the XXZ spin chain with unparallel boundary magnetic fields are derived in the framework of the algebraic Bethe ansatz. In the easy-plane case, we show the elementary excitations are some kind of spinons without definite spin because the U(1) symmetry is broken, while in the easy-axis ferromagnetic case a spiral state is realized in the ground state. The correlation functions, the spin torque as well as the spin voltage for the later case are also derived.
A novel Bethe ansatz scheme is proposed to calculate physical properties of quantum integrable systems without U(1)U(1)U(1) symmetry. As an example, the antiperiodic XXZ spin chain, a typical correlated many-body system embedded in a topological manifold, is examined. Conserved ``momentum'' and ``charge'' operators are constructed despite the absence of translational invariance and U(1)U(1)U(1) symmetry. The ground state energy and elementary excitations are derived exactly. It is found that two intrinsic fractional (one half) zero modes accounting for the double degeneracy exist in the eigenstates. The elementary excitations show quite a different picture from that of a periodic chain. This method can be applied to other quantum integrable models either with or without U(1)U(1)U(1) symmetry.