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arXiv 1206.1847quant-phcond-mat.stat-mechmath-phmath.MP
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高温下大自旋系统的非平凡玻色表象

A nontrivial bosonic representation of large spin systems at high temperatures

Yamen Hamdouni

摘要:

我们报道了自旋算符的非平凡玻色化方案。结果表明,在大的$N$极限下,在无限温度下,算符$\sum_{k=1}^N \hat s_{k\pm}/\sqrt{N}$的行为类似于产生算符和湮灭算符$a^†$和$a$,对应于热平衡的谐振子,其温度和频率由$\hbarω/k_B T=\ln 3$相关.发现$z$分量等价于另一个谐振子在零温度下占据其高斯基态的位置变量。将所得结果应用于有限温度下的海森堡XY哈密顿量。

英文摘要:

We report on a nontrivial bosonization scheme for spin operators. It is shown that in the large $N$ limit, at infinite temperature, the operators $\sum_{k=1}^N \hat s_{k\pm}/\sqrt{N}$ behave like the creation and annihilation operators, $a^†$ and $a$, corresponding to a harmonic oscillator in thermal equilibrium, whose temperature and frequency are related by $\hbarω/k_B T=\ln 3$. The $z$ component is found to be equivalent to the position variable of another harmonic oscillator occupying its ground Gaussian state at zero temperature. The obtained results are applied to the Heisenberg XY Hamiltonian at finite temperature.

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