Free energy asymptotics of the quantum Heisenberg spin chain

Marcin Napiórkowski, Robert Seiringer

Abstract We consider the ferromagnetic quantum Heisenberg model in one dimension, for any spin $$S\ge 1/2$$ 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.

P. Schlottmann, Kong-Ju-Bock Lee

M. Correggi, A. Giuliani

Joseph G. Conlon, Jan Philip Solovej

The authors discuss various asymptotic limits of the classical and quantum Heisenberg model. They give a new proof that the thermodynamic free energy of the quantum model converges to the free energy of the classical model in the limit of large spins. They also obtain Gaussian and free Bose gas limits for the classical and quantum models respectively.

Minoru Takahashi, Masahiro Shiroishi

Pengcheng Lu, Yi Qiao, Junpeng Cao +3 more

Abstract A new nonlinear integral equation (NLIE) describing the thermodynamics of the Heisenberg spin chain is derived based on the t − W relation of the quantum transfer matrices. The free energy of the system in a magnetic field is thus obtained by solving the NLIE. This method can be generalized to other lattice quantum integrable models. Taking the SU(3)-invariant quantum spin chain as an example, we construct the corre- sponding NLIEs and compute the free energy. The present results coincide exactly with those obtained via other methods previously.