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The spin-Peierls transition is modeled in the dimer phase of the spin-$1/2$ chain with exchanges $J_1$, $J_2 = alpha J_1$ between first and second neighbors. The degenerate ground state generates an energy cusp that qualitatively changes the dimerization $delta(T)$ compared to Peierls systems with nondegenerate ground states. The parameters $J_1 = 160$ K, $alpha = 0.35$ plus a lattice stiffness account for the magnetic susceptibility of CuGeO$_3$, its specific heat anomaly, and the $T$ dependence of the lowest gap.
The spin-Peierls transition at $T_{SP}$ of spin-$1/2$ chains with isotropic exchange interactions has previously been modeled as correlated for $T > T_{SP}$ and mean field for $T < T_{SP}$. We use correlated states throughout in the $J_1-J_2$ model w
The antiferromagnetic $J_1-J_2$ model is a spin-1/2 chain with isotropic exchange $J_1 > 0$ between first neighbors and $J_2 = alpha J_1$ between second neighbors. The model supports both gapless quantum phases with nondegenerate ground states and ga
The one-dimensional spin-S $J_1-J_2$ XY model is studied within the bosonization approach. Around the two limits ($J_2/J_1 ll 1,J_2/J_1 gg 1$) where a field theoretical analysis can be derived, we discuss the phases as well as the different phase tra
Strongly correlated systems with geometric frustrations can host the emergent phases of matter with unconventional properties. Here, we study the spin $S = 1$ Heisenberg model on the honeycomb lattice with the antiferromagnetic first- ($J_1$) and sec
Using density-matrix renormalization-group calculations for infinite cylinders, we elucidate the properties of the spin-liquid phase of the spin-$frac{1}{2}$ $J_1$-$J_2$ Heisenberg model on the triangular lattice. We find four distinct ground-states