Dimerizations in spin-$S$ antiferromagnetic chains with three-spin interaction

Abstract

We discuss spin-$S$ antiferromagnetic Heisenberg chains with three-spin interactions, next-nearest-neighbor interactions, and bond alternation. First, we prove rigorously that there exist parameter regions of the exact dimerized ground state in this system. This is a generalization of the Majumdar-Ghosh model to arbitrary $S$. Next, we discuss the ground-state phase diagram of the models by introducing several effective field theories and the universality classes of the transitions are described by the level-$2S$ $\mathrm{SU}(2)$ Wess-Zumino-Witten model and the Gaussian model. Finally, we determine the phase diagrams of $S=1$ and $S=3/2$ systems by using exact diagonalization and level spectroscopy.

7 pages, 5 figures

References in corpus (7)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Antiferromagnetic spin-S chains with exactly dimerized ground states
• Realization of higher Wess-Zumino-Witten models in spin chains
• Dimerizations in spin-$S$ antiferromagnetic chains with three-spin interaction
• Effective field theory with a $\theta$-vacua structure for 2d spin systems
• Mass ratio of elementary excitations in frustrated antiferromagnetic chains with dimerization

Cited by in corpus (17)

• Symmetry protection of critical phases and global anomaly in $1+1$ dimensions
• Dimerization transitions in spin-1 chains
• Spontaneous dimerization, critical lines, and short-range correlations in a frustrated spin-1 chain
• Dimerizations in spin-$S$ antiferromagnetic chains with three-spin interaction
• Floating, critical and dimerized phases in a frustrated spin-3/2 chain
• From SU(2)${}_5$ to SU(2)${}_3$ Wess-Zumino-Witten transitions in a frustrated spin-5/2 chain
• Phase diagram of the alternating-spin Heisenberg chain with extra isotropic three-body exchange interactions
• Dimerization and effective decoupling in two spin-1 generalizations of the spin-1/2 Majumdar-Ghosh chain
• Rigorous decoupling between edge states in frustrated spin chains and ladders
• Alternating-spin S=3/2 and sigma=1/2 Heisenberg chain with three-body exchange interactions
• Phase diagram study of a dimerized spin-S zig-zag ladder
• Realization of Wess-Zumino-Witten transitions with levels $k=6$ and $k=4$ in a frustrated spin-3 chain
• Heisenberg spin chains with additional isotropic three-site exchange interactions
• Local spin transfer torque and magnetoresistance in domain walls with variable width
• Confinement, deconfinement, and bound states in the spin-$1$ and spin-$3/2$ generalizations of the Majumdar--Ghosh chain
• Extended Ashkin-Teller transition in two coupled frustrated Haldane chains
• Deconfined criticality for the two-dimensional quantum S=1-spin model with the three-spin and biquadratic interactions