Free energy asymptotics of the quantum Heisenberg spin chain

We consider the ferromagnetic quantum Heisenberg model in one dimension, for any spin S >= 1/2. We give upper and lower bounds on the free energy, proving that at low temperature it is asymptotically equal to the one of an ideal Bose gas of magnons, as predicted by the spin-wave approximation. The trial state used in the upper bound yields an analogous estimate also in the case of two spatial dimensions, which is believed to be sharp at low temperature.

Automated summary

In this study, the ferromagnetic quantum Heisenberg model in one dimension was considered for spins greater than or equal to 1/2. Upper and lower bounds on the free energy were provided, showing that at low temperatures it approaches the free energy of an ideal Bose gas of magnons as predicted by the spin-wave approximation. The trial state used for the upper bound also yielded a similar estimate in two spatial dimensions, believed to be accurate at low temperatures.