Quantum versus classical behavior in the boundary susceptibility of the ferromagnetic Heisenberg chain

We calculate the temperature dependence of the boundary susceptibility χB for the quantum ferromagnetic Heisenberg chain by a modified spin-wave theory (MSWT). We find that χB diverges at low temperatures ∼- T-3 and therefore more rapidly and with opposite sign than the bulk susceptibility χbulk ∼ T-2. Our result for χB is identical in leading order with the result for the classical system. In next leading orders, however, quantum corrections to the classical result exist which are important to obtain a good description over a wide temperature range. For the S=1/2 case, we show that our full result from MSWT is in excellent agreement with numerical data obtained by the density-matrix renormalization group applied to transfer matrices. Finally, we discuss the quantum to classical crossover as well as consequences of our results for experiment in some detail.