Thermodynamics of Spin S = 1/2 Antiferromagnetic Uniform and   Alternating-Exchange Heisenberg Chains
  The magnetic susceptibility chi and specific heat C versus temperature T of the spin-1/2 antiferromagnetic alternating-exchange (J1 and J2) Heisenberg chain are studied for the entire range 0 \leq alpha \leq 1 of the alternation parameter alpha = J2/J1. For the uniform chain (alpha = 1), detailed comparisons of the high-accuracy chi(T) and C(T) Bethe ansatz data of Kluemper and Johnston are made with the asymptotically exact low-T field theory predictions of Lukyanov. QMC simulations and TMRG calculations of chi(alpha,T) are presented. From the low-T TMRG data, the spin gap Delta(alpha)/J1 is extracted for 0.8 \leq alpha \leq 0.995. High accuracy fits to all of the above numerical data are obtained. We examine in detail the theoretical predictions of Bulaevskii for chi(alpha,T) and compare them with our results. Our experimental chi(T) and C(T) data for NaV2O5 single crystals are modeled in detail. The chi(T) data above the spin dimerization temperature Tc = 34 K are not in agreement with the prediction for the uniform Heisenberg chain, but can be explained if there is a moderate ferromagnetic interchain coupling and/or if J changes with T. By fitting the chi(T) data, we obtain Delta(T = 0) = 103(2) K, alternation parameter delta(0) = (1 - alpha)/(1 + alpha) = 0.034(6) and average exchange constant J(0) = 640(80) K. The delta(T) and Delta(T) are derived from the data. A spin pseudogap with a large magnitude \approx 0.4 Delta(0) is consistently found just above Tc, which decreases with increasing T. Analysis of our C(T) data indicates that at Tc, at least 77% of the entropy change due to the transition at Tc and associated order parameter fluctuations arise from the lattice and/or charge degrees of freedom and less than 23% from the spin degrees of freedom. 
D.C. Johnston, R.K. Kremer, M. Troyer, X. Wang, A. Kl\"umper, S.L.   Bud'ko, A.F. Panchula, P.C. Canfield