A comparative study of the phase diagrams of spin-$\frac{1}{2}$ and spin-$1$ antiferromagnetic chains with dimerization and frustration

Abstract

We use the density matrix renormalization group method to study the ground state `phase' diagram and some low-energy properties of isotropic antiferromagnetic spin-$\frac{1}{2}$ and spin-$1$ chains with a next-nearest neighbor exchange $J_2$ and an alternation $\delta$ of the nearest neighbor exchanges. In the spin-$\frac{1}{2}$ chain, the system is gapless for $\delta =0$ and $J_2<J_{2c}=0.241$, and is gapped everywhere else in the $J_2-\delta$ plane. At $J_{2c}$, for small $\delta$, the gap increases as ${\delta }^{\alpha }$, where $\alpha =0.667\pm 0.001$. $2J_2+\delta =1$ is a disorder line. To the left of this line, the structure factor $S(q)$ peaks at $q_{max}=\pi$ (Neel `phase'), while to the right, $q_{max}$ decreases from $\pi$ to $\pi /2$ (spiral `phase') as $J_2$ increases. There is also a `$\uparrow \uparrow \downarrow \downarrow$ phase' for large values of both $J_2$ and $\delta$. In the spin-$1$ case, we find a line running from a gapless point at $(J_2,\delta )=(0,0.25\pm 0.01)$ upto a `gapless' point at $(0.73\pm 0.005,0)$ such that the open chain ground state is four-fold degenerate below the line and is unique above it. There is a disorder line in this case also and it has the same equation as in the spin-$\frac{1}{2}$ case, but the line ends at about $\delta =0.136$. Similar to the spin-$\frac{1}{2}$ case, to the left of this line, the peak in the structure factor is at $\pi$ (Neel `phase'), while to the right of the line, it is at less than $\pi$ (spiral `phase'). For $\delta =1$, the system corresponds to a spin ladder and the system is gapped for all values of the interchain coupling for both spin-$\frac{1}{2}$ and spin-$1$ ladders.

arXiv comment16 pages in latex; 9 figures available on request

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Cited by in corpus (9)

• The density-matrix renormalization group
• Frustration and Multicriticality in the Antiferromagnetic Spin-1 Chain
• On the dynamics of coupled S=1/2 antiferromagnetic zig-zag chains
• Elementary excitations in the gapped phase of a frustrated S=1/2 spin ladder: from spinons to the Haldane triplet
• Quantum magnets with weakly confined spinons: Multiple length scales and quantum impurities
• Quantum phases of dimerized and frustrated Heisenberg spin chains with s = 1/2, 1 and 3/2: an entanglement entropy and fidelity study
• Sequential quantum phase transitions in $J_1$-$J_2$ Heisenberg chains with integer spins ($S>1$): Quantized Berry phase and valence-bond solids
• Field Theories of Frustrated Heisenberg Antiferromagnets
• One-dimensional physics of the frustrated quantum magnet PHCC