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arXiv:2211.01683 · SciPost Physics

Exact physical quantities of a competing spin chain in the thermodynamic limit

Pengcheng Lu, Yi Qiao, Junpeng Cao, Wen‐Li Yang

Published Aug 10, 2023• 0 citations
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Abstract

We study the exact physical quantities of a competing spin chain which contains many interesting and meaningful couplings including the nearest neighbor, next nearest neighbor, chiral three spins, Dzyloshinsky-Moriya interactions and unparallel boundary magnetic fields in the thermodynamic limit. We obtain the density of zero roots, surface energies and elementary excitations in different regimes of model parameters. Due to the competition of various interactions, the surface energy and excited spectrum show many different pictures from those of the Heisenberg spin chain.

DOI
10.21468/scipostphys.15.2.060

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We study the exact physical quantities of a competing spin chain which contains many interesting and meaningful couplings including the nearest neighbor, next nearest neighbor, chiral three spins, Dzyloshinsky-Moriya interactions and unparallel boundary magnetic fields in the thermodynamic limit. We obtain the density of zero roots, surface energies and elementary excitations in different regimes of model parameters. Due to the competition of various interactions, the surface energy and excited spectrum show many different pictures from those of the Heisenberg spin chain.
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Abstract We obtain the exact solution of an anisotropic quantum spin chain including nearest neighbor (NN), next nearest neighbor (NNN), chiral three-spin interactions and non-diagonal boundary terms. Because the NNN couplings are involved, we find that the off-diagonal boundary reflections can not only induce the anisotropic Dzyloshinsky–Moriya interactions at boundaries but also enhance the anisotropy of first and last bonds. These properties are absent if only the NN spin-exchanging interactions are considered. Due to that the U (1) symmetry is broken, we analytically solve the system by using the off-diagonal Bethe ansatz. The inhomogeneous T − Q relation, energy spectrum and associated Bethe ansatz equations are given explicitly. This paper provides an universal scheme to construct new integrable models with certain interesting interactions.
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.
A novel Bethe ansatz scheme is proposed to investigate the exact physical properties of an integrable anisotropic quantum spin chain with competing interactions among the nearest, next nearest neighbor and chiral three spin couplings, where the boundary condition is the twisted one. The eigenvalue of the transfer matrix is characterized by its zero roots instead of the traditional Bethe roots. Based on the exact solution, the conserved momentum and charge operators of this U(1)-symmetry broken system are obtained. The ground state energy and density of rapidities are calculated. It is found that there exist three kinds of elementary excitations and the corresponding dispersion relations are obtained, which gives a different picture from that with periodic boundary condition.
The exact elementary excitations in a typical U(1)U(1)U(1) symmetry broken quantum integrable system, that is the twisted ${J}_{1}\ensuremath{-}{J}_{2}$ spin chain with nearest-neighbor, next nearest neighbor, and chiral three spin interactions, are studied. The main technique is that we quantify the energy spectrum of the system by the zero roots of the transfer matrix instead of the traditional Bethe roots. From the numerical calculation and singularity analysis, we obtain the patterns of zero roots. Based on them, we analytically obtain the ground state energy and the elementary excitations in the thermodynamic limit. We find that the system also exhibits the nearly degenerate states in the regime of $\ensuremath{\eta}\ensuremath{\in}\mathbb{R}$, where the nearest-neighbor couplings among the zzz direction are ferromagnetic. More careful study shows that the competing of interactions can induce the gapless low-lying excitations and quantum phase transition in the antiferromagnetic regime with $\ensuremath{\eta}\ensuremath{\in}\mathbb{R}+i\ensuremath{\pi}$.
A bstract The thermodynamic limits of the XYZ spin chain with periodic or twisted boundary conditions are studied. By using the technique of characterizing the eigenvalue of the transfer matrix by the T − Q relation and by the zeros of the associated polynomial, we obtain the constraints of the Bethe roots and the zeros for the eigenvalues. With the help of structure of Bethe roots, we obtain the distribution patterns of zeros. Based on them, the physical quantities such as the surface energy and excitation energy are calculated. We find that both of them depend on the parity of sites number due to the topological long-range Neel order on the Mobius manifold in the spin space. We also check our results with those obtaining by the density matrix renormalization group. The method provided in this paper can be applied to study the thermodynamic properties at the thermal equilibrium state with finite temperature.