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arXiv 2012.03088quant-phcond-mat.stat-mech
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复杂网络中的超辐射相变

Superradiant phase transition in complex networks

Andrei Yu. Bazhenov, Dmitriy V. Tsarev, Alexander P. Alodjants

摘要:

本文考虑了Dicke-Ising模型的超辐射相变问题,它推广了Dicke和伊辛模型在自旋-自旋相互作用下的退火复杂网络.该模型考虑了自旋(二能级)系统与外部经典(磁场)和量子化(横向)场之间的相互作用。我们研究定期,随机和无标度的网络结构,其特征在于三角函数,随机(泊松),幂律指数度分布,分别。为了描述顺磁(PM)-铁磁(FM)和超辐射(SR)相变,我们引入了两个序参量:总加权自旋z分量和归一化横场振幅,它们分别对应于z和x方向的自发磁化强度。由于自旋相互作用和网络中的有限尺寸效应之间的相互作用,我们首先阐明了在PM-FM相变存在下SR态的新特征。我们揭示了SR相变的临界温度从对应于临界节点数的某个值单调增长。对于无标度网络,我们发现这个临界温度随着度指数的增加而升高,同时伴随着量子横向场中自发磁化的建立和z方向集体自旋分量的消失。此外,我们还建立了当临界温度接近零时,自旋系统发生量子相变的网络参数条件。的基本特征,其中涉及的经典和量子场参数的临界值,讨论了在此限制的超辐射相的发生。

英文摘要:

In this work we consider a superradiant phase transition problem for the Dicke-Ising model, which generalizes the Dicke and Ising models for annealed complex networks presuming spin-spin interaction. The model accounts the interaction between a spin (two-level) system and external classical (magnetic) and quantized (transverse) fields. We examine regular, random, and scale-free network structures characterized by the delta-function, random (Poisson), and power-law exponent degree distributions, respectively. To describe paramagnetic (PM) - ferromagnetic (FM) and superradiant (SR) phase transitions we introduce two order parameters: the total weighted spin z-component and the normalized transverse field amplitude, which correspond to the spontaneous magnetization in z and x directions, respectively. Due to the interplay between the spin interaction and the finite size effects in the networks we first elucidate novel features of the SR state in the presence of the PM-FM phase transition. We reveal that the critical temperature of the SR phase transition grows monotonically from some certain value that corresponds to the critical number of nodes. For the scale-free networks we find that this critical temperature rises with the degree exponent increase accompanied both by establishing spontaneous magnetization in a quantum transverse field and vanishing of the collective spin component in z direction. In addition, we establish the conditions for the network parameters to obtain a quantum phase transition in the spin system when the critical temperature approaches zero. The fundamental features, which involve critical values of the classical and quantum field parameters, are discussed for the occurrence of the superradiance phase in this limit.

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