Gapless line for the anisotropic Heisenberg spin-1/2 chain in a magnetic field and the quantum axial next-nearest-neighbor Ising Chain

Abstract

We study the anisotropic Heisenberg (XYZ) spin-1/2 chain placed in a magnetic field pointing along the x-axis. We use bosonization and a renormalization group analysis to show that the model has a non-trivial fixed point at a certain value of the XY anisotropy a and the magnetic field h. Hence, there is a line of critical points in the (a,h) plane on which the system is gapless, even though the Hamiltonian has no continuous symmetry. The quantum critical line corresponds to a spin-flop transition; it separates two gapped phases in one of which the Z_2 symmetry of the Hamiltonian is broken. Our study has a bearing on one of the transitions of the axial next-nearest neighbor Ising (ANNNI) chain in a transverse magnetic field. We also discuss the properties of the model when the magnetic field is increased further, in particular, the disorder line on which the ground state is a direct product of single spin states.

arXiv commentExpanded version of cond-mat/0208216; Revtex, 7 pages, 2 eps figures

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• Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
• Spin Ladder with Anisotropic Ferromagnetic Legs in a Transverse Magnetic Field
• Floating Phase in 2D ANNNI Model
• Quantum fidelity approach to the ground state properties of the 1D ANNNI model in a transverse field
• Fermionic Magic Resources of Quantum Many-Body Systems
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• From frustrated insulators to correlated anisotropic metals: charge ordering and quantum criticality in coupled chain systems
• Spin-spin Correlation in Some Excited States of Transverse Ising Model
• Quantum simulation of spin-1/2 XYZ model using solid-state spin centers