Exact solution of an integrable anisotropic $J_1-J_2$ spin chain model

Abstract

An integrable anisotropic Heisenberg spin chain with nearest-neighbour couplings, next-nearest-neighbour couplings and scalar chirality terms is constructed. After proving the integrability, we obtain the exact solution of the system. The ground state and the elementary excitations are also studied. It is shown that the spinon excitation of the present model possesses a novel triple arched structure. The elementary excitation is gapless if the anisotropic parameter $\eta$ is real while the elementary excitation has an enhanced gap by the next-nearest-neighbour and chiral three-spin interactions if the anisotropic parameter $\eta$ is imaginary. The method of this paper provides a general way to construct new integrable models with next-nearest-neighbour interactions.

arXiv comment10 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1812.09316

References in corpus (16)

• Dimerization and Incommensurate Spiral Spin Correlations in the Zigzag Spin Chain: Analogies to the Kondo Lattice
• Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal Operators
• Numerical and approximate analytical results for the frustrated spin-1/2 quantum spin chain
• PT Symmetry on the Lattice: The Quantum Group Invariant XXZ Spin-Chain
• Chiral Spin Liquids in Arrays of Spin Chains
• Phase Diagram of the One Dimensional $S=1/2$ $XXZ$ model with Ferromagnetic nearest-neighbor and Antiferromagnetic next-nearest neighbor interactions
• Properties of the chiral spin liquid state in generalized spin ladders
• Second order quantum renormalisation group of XXZ chain with next nearest neighbour interactions
• The Staggered Six-Vertex Model: Conformal Invariance and Corrections to Scaling
• The $Z_2$ staggered vertex model and its applications
• Integrable models of coupled Heisenberg chains
• Integrable Chain Model with Additional Staggered Model Parameter
• A model of chiral spin liquids with Abelian and non-Abelian topological phases
• Spinon statistics in integrable spin-S Heisenberg chains
• Magnetocaloric effect in the spin-$1/2$ chain with competing interactions
• Thermodynamics of quantum spin chains with competing interactions

Cited by in corpus (2)

• Augmenting Density Matrix Renormalization Group with Disentanglers
• Exact solution of a anisotropic $J_1-J_2$ spin chain with antiperiodic boundary condition