Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió, Alagoas, Brazil.
Phys Rev E. 2017 Jun;95(6-1):062105. doi: 10.1103/PhysRevE.95.062105. Epub 2017 Jun 5.
Recent experimental progress on the realization of quantum systems with highly controllable long-range interactions has impelled the study of quantum phase transitions in low-dimensional systems with power-law couplings. Long-range couplings mimic higher-dimensional effects in several physical contexts. Here, we provide the exact relation between the spectral dimension d at the band bottom and the exponent α that tunes the range of power-law hoppings of a one-dimensional ideal lattice Bose gas. We also develop a finite-size scaling analysis to obtain some relevant critical exponents and the critical temperature of the BEC transition. In particular, an irrelevant dangerous scaling field has to be taken into account when the hopping range is sufficiently large to make the effective dimensionality d>4.
最近在实现具有高度可控远程相互作用的量子系统方面的实验进展，推动了对具有幂律耦合的低维系统中的量子相变的研究。远程耦合在几个物理背景下模拟了更高维度的效应。在这里，我们提供了在能带底部的谱维度 d 与调节一维理想晶格玻色气体的幂律跳跃范围的指数 α 之间的精确关系。我们还开发了有限大小标度分析，以获得一些相关的临界指数和 BEC 相变的临界温度。特别是，当跳跃范围足够大以使有效维度 d>4 时，必须考虑一个无关紧要的危险标度场。
