Finite-size scaling exponents in the Dicke model
Finite-size scaling exponents in the Dicke model
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DOI：
10.1209/epl/i2006-10041-9
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发表时间：
2005-10
期刊：
影响因子：
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通讯作者：
J. Vidal;S. Dusuel
中科院分区：
文献类型：
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作者：
J. Vidal;S. Dusuel
我们考虑了迪凯模型中的有限尺寸修正，并确定了基态能量或差距等几个量在临界点处的标度指数。因此，我们使用角动量的Holstein-Primakoff表示，并引入正则变换来对角化正常相位中的哈密顿量。正如已经在几个系统中观察到的那样，这些修正在过渡点处是奇异的，从而导致非平凡指数。我们表明，对于原子可观测量，这些指数与Lipkin-Meshkov-Glick模型中的指数相同，与数值结果一致。我们还研究了与辐射模相关的序参量的行为，并表明它是由与原子相同的标度变量驱动的。
We consider the finite-size corrections in the Dicke model and determine the scaling exponents at the critical point for several quantities such as the ground-state energy or the gap. Therefore, we use the Holstein-Primakoff representation of the angular momentum and introduce a canonical transformation to diagonalize the Hamiltonian in the normal phase. As already observed in several systems, these corrections turn out to be singular at the transition point and thus lead to nontrivial exponents. We show that for the atomic observables, these exponents are the same as in the Lipkin-Meshkov-Glick model, in agreement with numerical results. We also investigate the behavior of the order parameter related to the radiation mode and show that it is driven by the same scaling variable as the atomic one.