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Free energy asymptotics of the quantum Heisenberg spin chain
Letters in Mathematical Physics ( IF 1.2 ) Pub Date : 2021-03-09 , DOI: 10.1007/s11005-021-01375-4
Marcin Napiórkowski , Robert Seiringer

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



中文翻译:

量子海森堡自旋链的自由能渐近性

对于任何自旋\(S \ ge 1/2 \),我们都在一维考虑铁磁量子海森堡模型。我们给出了自由能的上限和下限,证明了在低温下,它渐近地等于理想的玻色子马农信号之一,如自旋波近似所预测的那样。在两个空间维度的情况下,上限中使用的试用状态也产生了类似的估计值,据信在低温下这是很明显的。

更新日期:2021-03-09
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