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首页> 外文期刊>Zeitschrift fur Physik, B. Condensed Matter >Quantum rotors with regular frustration and the quantum Lifshitz point
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Quantum rotors with regular frustration and the quantum Lifshitz point

机译：规则挫折的量子转子和量子Lifshitz点

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We have discussed the zero-temperature quantum phase transition in n-component quantum rotor Hamiltonian in the presence of regular frustration in the interaction. The phase diagram consists of ferromagnetic, helical and quantum paramagnetic phase, where the ferro-para and the helical-para phase boundary meets at a multicritical point called a (d, m) quantum Lifshitz point where (d, m) indicates that the m of the d spatial dimensions incorporate frustration. We have studied the Hamiltonian in the vicinity of the quantum Lifshitz point in the spherical limit and also studied the renormalisation group flow behaviour using standard momentum space renormalisation technique (for finite n). In the spherical limit (n → ∞) one finds that the helical phase does not exist in the presence of any nonvanishing quantum fluctuation for m = d though the quantum Lifshitz point exists for all d > 1 + m/2, and the upper critical dimensionality is given by d_u = 3 + m/s. The scaling behaviour in the neighbourhood of a quantum Lifshitz point in d dimensions is consistent with the behaviour near the classical Lifshitz point in (d + z) dimensions. The dynamical exponent of the quantum Hamiltonian z is unity in the case of anisotropic Lifshitz point (d > m) whereas z = 2 in the case of isotropic Lifshitz point (d = m). We have evaluated all the exponents using the renormalisation flow equations along-with the scaling relations near the quantum Lifshitz point. We have also obtained the exponents in the spherical limit (n → ∞). It has also been shown that the exponents in the spherical model are all related to those of the corresponding Gaussian model by Fisher renormalisation.
机译：我们已经讨论了在相互作用中存在规则挫折的情况下，n分量量子转子哈密顿量中的零温度量子相变。相图由铁磁，螺旋和量子顺磁相组成，其中铁对和螺旋对相边界在称为（d，m）量子利夫谢兹点的多临界点相遇，其中（d，m）表示m d个空间维度中包含挫折感。我们已经研究了球形极限中的量子Lifshitz点附近的哈密顿量，并且还使用标准动量空间重归一化技术（对于有限n）研究了重归一化群流动行为。在球形极限（n→∞）中，发现尽管存在对于所有d> 1 + m / 2的量子Lifshitz点，但对于m = d，在没有任何消失的量子涨落的情况下不存在螺旋相。尺寸由d_u = 3 + m / s给出。 d维量子Lifshitz点附近的缩放行为与（d + z）维经典Lifshitz点附近的行为一致。在各向异性Lifshitz点（d> m）的情况下，量子哈密顿量z的动力学指数为1，而在各向同性Lifshitz点（d = m）的情况下z = 2。我们已经使用重归一化流方程以及靠近量子Lifshitz点的比例关系来评估了所有指数。我们还获得了球极限（n→∞）中的指数。还已经表明，通过费希尔重新归一化，球形模型中的指数都与相应的高斯模型中的指数相关。

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