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) between second neighbors. The model supports both gapless quantum phases with nondegenerate ground states and gapped phases with Delta(alpha) > 0 and doubly degenerate ground states. Exact thermodynamics is limited to alpha= 0, the linear Heisenberg antiferromagnet (HAF). Exact diagonalization of small systems at frustration a followed by density matrix renormalization group calculations returns the entropy density S(T, alpha, N) and magnetic susceptibility chi(T, alpha, N) of progressively larger systems up to N = 96 or 152 spins. Convergence to the thermodynamic limit, S(T, alpha) or chi(T, alpha), is demonstrated down to T/J similar to 0.01 in the sectors alpha < 1 and alpha > 1. S(T, alpha) yields the critical points between gapless phases with S'(0, alpha) > 0 and gapped phases with S'(0, alpha) = 0. The S'(T, alpha) maximum at T* (alpha) is obtained directly in chains with large Delta(alpha) and by extrapolation for small gaps. A phenomenological approximation for S(T, alpha) down to T = 0 indicates power-law deviations T-gamma(alpha) from exp[-Delta(alpha)/T] with exponent gamma (alpha) that increases with alpha. The chi(T, alpha) analysis also yields power-law deviations, but with exponent eta(alpha) that decreases with alpha. Spin correlation functions account for S(T, alpha) differences between frustration alpha < 1 within a chain and alpha > 1 between HAFs on sublattices. S(T, alpha) and the spin density rho(T, alpha) = 4T chi(T, alpha) probe the thermal and magnetic fluctuations, respectively, of strongly correlated spin states. Gapless chains have constant S(T, alpha)/rho(T, alpha) for T < 0.10. Remarkably, the ratio decreases (increases) with T in chains with large (small) Delta(alpha).

Automated summary

The study of the antiferromagnetic J(1) - J(2) model involves extensive research and calculations, revealing the relationship between different thermodynamic properties and the thermodynamic results for specific parameters.