Abstract
We study the phase diagram of spin-1 antiferromagnetic chain with isotropic antiferromagnetic interactions decaying with a power-law $\propto r^{-\alpha}$ ($\alpha\ge 1$) accompanied by modulated single-ion anisotropy. Employing the techniques of the density-matrix renormalization group, effects of long-range interactions and single-ion anisotropy on a variety of correlations are investigated. In order to check the consistency, the fidelity susceptibilities are evaluated across quantum phase transitions. The quantum critical points are faithfully detected and orders of phase transitions are determined. The correlation-length critical exponent is extracted from scaling functions of the fidelity susceptibility. The presence of long-range interactions leads to quantitative change of the phase boundaries and reduces the order of phase transition under certain conditions. A direct first-order transition between the periodic N\'eel phase and the large-$D$ phase occurs for slowly decaying antiferromagnetic interactions.
Highlights
The Haldane phase [1,2] of the one-dimensional (1D) antiferromagnetic (AF) spin-1 (S = 1) chain has received continued attention as it is closely related to the breaking of a hidden Z2 ⊗ Z2 symmetry [3] through a nonlocal unitary transformation
We study the phase diagram of a spin-1 antiferromagnetic chain with isotropic antiferromagnetic interactions decaying with a power law ∝r−α (α 1) accompanied by modulated single-ion anisotropy
We investigated the quantum phase transitions in the one-dimensional spin-1 chains with long-range antiferromagnetic interactions decaying with a power law and modulated single-ion anisotropy by using the density-matrix renormalization group technique
Summary
OLESboundary condition and provides crucial insight into the symmetry-protected topological (SPT) order Such a general bilinear-biquadratic Hamiltonian leads to a dimerized spin-1 chain for a range of parameters [10]. We go further and analyze the frustrated spin-1 chain with infinite-range AF correlations which decay algebraically in the presence of a superposition of uniform and alternating uniaxial single-ion anisotropy. The present work addresses primarily the QPTs in the spin-1 chains with long-range interactions and modulated single-ion anisotropy. We employ here the fidelity susceptibility and establish a rich phase diagram of a spin-1 chain by changing the uniform and alternating single-ion anisotropy.
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