By means of thermal expansion and specific heat measurements on the high-pressure phase of $(\mathrm{VO}{)}_2{\mathrm{P}}_2{\mathrm{O}}_7$, the effects of two energy scales of the weakly dimerized antiferromagnetic $S=1/2$ Heisenberg chain are explored. The low-energy scale, given by the spin gap $\Delta$, is found to manifest itself in a pronounced thermal expansion anomaly. A quantitative analysis, employing the density-matrix renormalization-group approach for transfer matrices calculations, shows that this feature originates from changes in the magnetic entropy with respect to $\Delta$, $\partial S^m/\partial \Delta$. This term, inaccessible by specific heat, is visible only in the weak-dimerization limit, where it reflects peculiarities of the excitation spectrum and its sensitivity to variations in $\Delta$.

• Received 15 March 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.057204