Low-temperature thermodynamics of the antiferromagnetic J1−J2 model: Entropy, critical points, and spin gap

The antiferromagnetic $J_1-J_2$ model is a spin-1/2 chain with isotropic exchange $J_1 > 0$ between first neighbors and $J_2 = \alpha J_1$ second neighbors. supports both gapless quantum phases nondegenerate ground states gapped $\Delta(\alpha) doubly degenerate states. Exact thermodynamics limited to $\alpha 0$, the linear Heisenberg antiferromagnet (HAF). diagonalization of small systems at frustration $\alpha$ followed by density matrix renormalization group (DMRG) calculations returns entropy $S(T,\alpha,N)$ magnetic susceptibility $\chi(T,\alpha,N)$ progressively larger up $N 96$ or 152 spins. Convergence limit, $S(T,\alpha)$ $\chi(T,\alpha)$, demonstrated down $T/J \sim 0.01$ in sectors < 1$ 1$. yields critical points $S^\prime(0,\alpha) 0$. $S^\prime(T,\alpha)$ maximum $T^*(\alpha)$ obtained directly chains large $\Delta(\alpha)$ extrapolation for gaps. A phenomenological approximation $T indicates power-law deviations $T^{-\gamma(\alpha)}$ from $\exp(-\Delta(\alpha)/T)$ exponent $\gamma(\alpha)$ that increases $\alpha$. $\chi(T,\alpha)$ analysis also deviations, but $\eta(\alpha)$ decreases spin $\rho(T,\alpha) 4T\chi(T,\alpha)$ probe thermal fluctuations, respectively, strongly correlated Gapless have constant $S(T,\alpha)/\rho(T,\alpha)$ 0.10$. Remarkably, ratio (increases) $T$ (small) $\Delta(\alpha)$.