标题： 长程迪克-伊辛模型中恶魔阶梯的熔化 显示英文标题

标题： Melting of devil's staircases in the long-range Dicke-Ising model

摘要： 我们为具有与单个玻色模式线性耦合的反铁磁长程伊辛模型在正方格子和三角格子上的量子相图进行了研究。 对于零耦合情况，基态磁化率随着纵向场的变化形成磁化平台的恶魔阶梯结构。 除了在强光物质耦合下具有有限光子密度的顺磁超辐射相外，长程相互作用导致了大量中间相的出现，这些相破坏了平移对称性，同时具有有限的光子密度。 我们应用了一种基于原胞的平均场计算方法，该方法能够捕捉到所有可能的磁性原胞，直到选定的范围。 此外，我们利用非超辐射相到有效迪克模型的精确映射，计算了向超辐射相转变的相变上限。 最后，为了定量处理量子涨落，我们采用了一种广义的虫洞量子蒙特卡洛算法。 我们讨论了这三种方法如何协同使用。 在计算出的相图中，我们看到了由长程相互作用引起的几个特征：不同磁序正常相的恶魔阶梯以及超越近邻相互作用发现的非平凡磁序超辐射相。 例如，在正方格子上存在一个具有三个亚晶格磁序的超辐射相，在三角格子上存在每个原胞包含四个位点的超辐射威格纳晶体。 我们发现具有相同（不同）磁序的正常相与超辐射相之间的转变是二级相变，具有迪克普适性（一级相变）。 此外，在超辐射相之间我们发现了第一级相变，除了特别突出的区域，我们发现有迹象表明其行为为二级相变。 显示英文摘要

摘要： We present quantum phase diagrams for the antiferromagnetic long-range Ising model with a linear coupling to a single bosonic mode on the square and triangular lattice. For zero coupling, the ground-state magnetization forms a devil's staircase structure of magnetization plateaux as a function of a longitudinal field. Apart from a paramagnetic superradiant phase with a finite photon density at strong light-matter couplings, the long-range interactions lead to a plethora of intermediate phases that break the translational symmetry and have a finite photon density at the same time. We apply an adaption of the unit-cell-based mean-field calculations, which captures all possible magnetic unit cells up to a chosen extent. Further, we exploit an exact mapping of the non-superradiant phases to an effective Dicke model to calculate upper bounds for phase transitions towards superradiant phases. Finally, to treat quantum fluctuations in a quantitative fashion, we employ a generalized wormhole quantum Monte Carlo algorithm. We discuss how these three methods are used in a cooperative fashion. In the calculated phase diagrams we see several features arising from the long-range interactions: The devil's staircases of distinct magnetically ordered normal phases and non-trivial magnetically ordered superradiant phases beyond the findings for nearest-neighbor interactions. Examples are a superradiant phase with a three-sublattice magnetic order on the square lattice and the superradiant Wigner crystal with four sites per unit cell on the triangular lattice. We find the transition between normal and superradiant phases with the same (different) magnetic order to be of second order with Dicke universality (first order). Further, between superradiant phases we find first-order phase transitions, besides specially highlighted regimes for which we find indications for second-order behavior.