arXiv 1002.02522010-02quant-ph

自旋与玻色子耦合的精确可解模型中量子相变的离子阱模拟

Ion-trap simulation of the quantum phase transition in an exactly solvable model of spins coupled to bosons

Gian Luca Giorgi, Simone Paganelli, Fernando Galve

发表信息：: Physical Review A 81, 052118 (2010)
DOI：: 10.1103/PhysRevA.81.052118

摘要：

已知捕获离子的阵列可用于有效地模拟各种多体量子系统。在这里，我们展示了如何建立一个模型，表示一个自旋链与玻色子相互作用，这是完全可解的。研究了零温下该模型的精确能谱和基态性质。我们表明，当自旋和玻色子之间的耦合达到一个临界值，这对应于在能谱中的一个能级交叉的量子相变发生。一旦达到临界点，基态中玻色子激发的数量（可以假定为序参量）开始不同于零。玻色子模式的布居伴随着自旋的宏观磁化。这种双重效应可以代表用于相变检测的有用资源，因为对声子的测量可以给出关于自旋系统的相位的信息。在绝热状态下给出了有限温度相图。

英文摘要：

It is known that arrays of trapped ions can be used to efficiently simulate a variety of many-body quantum systems. Here, we show how it is possible to build a model representing a spin chain interacting with bosons which is exactly solvable. The exact spectrum of the model at zero temperature and the ground state properties are studied. We show that a quantum phase transition occurs when the coupling between spins and bosons reaches a critical value, which corresponds to a level crossing in the energy spectrum. Once the critical point is reached, the number of bosonic excitations in the ground state, which can be assumed as an order parameter, starts to be different from zero. The population of the bosonic mode is accompanied by a macroscopic magnetization of the spins. This double effect could represent an useful resource for the phase transition detection since a measure on the phonon can give information about the phase of the spin system. A finite temperature phase diagram is also given in the adiabatic regime.

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