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arXiv:2211.05549 · Physical review. D/Physical review. D.

Elementary excitations in an integrable twisted J1−J2 spin chain in the thermodynamic limit

Wei Wang, Yi Qiao, Ronghua Liu, Wu‐Ming Liu, Junpeng Cao

Published Mar 6, 2023• 2 citations
arXivHTMLPDF

Abstract

The exact elementary excitations in a typical $U(1)$ 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 $z$ 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 $\ensuremath{\eta}\ensuremath{\in}\mathbb{R}+i\ensuremath{\pi}$.

DOI
10.1103/physrevd.107.056005

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We construct an integrable quantum spin chain that includes the nearest-neighbor, next-nearest-neighbor, chiral three-spin couplings, Dzyloshinsky–Moriya interactions and unparallel boundary magnetic fields. Although the interactions in bulk materials are isotropic, the spins nearby the boundary fields are polarized, which induce the anisotropic exchanging interactions of the first and last bonds. The U(1) symmetry of the system is broken because of the off-diagonal boundary reflections. Using the off-diagonal Bethe ansatz, we obtain an exact solution to the system. The inhomogeneous T–Q relation and Bethe ansatz equations are given explicitly. We also calculate the ground state energy. The method given in this paper provides a general way to construct new integrable models with certain interesting interactions.
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Exact solution of an integrable J1−J2J_1-J_2J1​−J2​ spin chain model
An integrable Heisenberg spin chain with nearest-neighbour couplings, next-nearest-neighbour couplings and Dzyaloshinski-Moriya interacton is constructed. The integrability of the model is proven. Based on the Bethe Ansatz solutions, the ground state and the elementary excitations are studied. It is shown that the spinon excitation spectrum of the present system possesses a novel triple arched structure. The method provided in this paper is general to construct new integrable models with next-nearest-neighbour couplings.