粒子-空穴对称性和脏玻色子问题
Particle-hole symmetry and the dirty boson problem
摘要：
本文研究了粒子-空穴对称性对玻色子在淬冷随机介质中零温超流性起始所对应的各种量子相变普适性类的作用。这个问题在d空间维度的功能积分公式产生一个（d+1）维经典XY模型扩展的障碍-所谓的随机杆问题。粒子-空穴的对称性可以通过增加非零的位能而被打破。我们可以区分出三种情况：（i）精确的粒子-空穴对称性，在这种情况下，格位能量全部消失;（ii）统计的粒子-空穴对称性，在这种情况下，格位能量分布关于零对称，平均消失;（iii）完全不存在粒子-空穴对称性，在这种情况下，分布是通用的。我们探讨在每种情况下的性质的激发在非超流莫特绝缘和玻色玻璃相。我们发现，玻色玻璃的可压缩性，这有一个时间自旋刚度或超流密度的解释，是积极的情况下（ii）和（iii），但它消失了一个基本的奇异性作为完整的粒子-空穴对称性恢复。然后，我们专注于临界点和讨论的相关性类型（ii）粒子-空穴对称性破缺扰动的随机棒临界行为。我们认为，类型（iii）的扰动是无关的类型（ii）的临界行为：统计对称性恢复在大尺度上接近临界点，和情况（ii），因此描述了脏玻色子不动点。为了研究更高的维度，我们试图将Dorogovtsev-Cardy-Boyanovsky双展开技术推广到这个问题，并取得了部分成功。这种技术提供的定性的重整化群流图是相当引人注目的。
英文摘要：
We study the role of particle-hole symmetry on the universality class of various quantum phase transitions corresponding to the onset of superfluidity at zero temperature of bosons in a quenched random medium. The functional integral formulation of this problem in d spatial dimensions yields a (d+1)-dimensional classical XY-model with extended disorder--the so-called random rod problem. Particle-hole symmetry may then be broken by adding nonzero site energies. We may distinguish three cases: (i) exact particle-hole symmetry, in which the site energies all vanish, (ii) statistical particle-hole symmetry in which the site energy distribution is symmetric about zero, vanishing on average, and (iii) complete absence of particle-hole symmetry in which the distribution is generic. We explore in each case the nature of the excitations in the non-superfluid Mott insulating and Bose glass phases. We find that the Bose glass compressibility, which has the interpretation of a temporal spin stiffness or superfluid density, is positive in cases (ii) and (iii), but that it vanishes with an essential singularity as full particle-hole symmetry is restored. We then focus on the critical point and discuss the relevance of type (ii) particle-hole symmetry breaking perturbations to the random rod critical behavior. We argue that a perturbation of type (iii) is irrelevant to the resulting type (ii) critical behavior: the statistical symmetry is restored on large scales close to the critical point, and case (ii) therefore describes the dirty boson fixed point. To study higher dimensions we attempt, with partial success, to generalize the Dorogovtsev-Cardy-Boyanovsky double epsilon expansion technique to this problem. The qualitative renormalization group flow picture this technique provides is quite compelling.
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