Particle-hole symmetry and the dirty boson problem
Particle-hole symmetry and the dirty boson problem
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粒子孔对称性和脏玻色子问题
DOI：
10.1103/physrevb.77.214516
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发表时间：
2008
影响因子：
3.7
通讯作者：
R. Mukhopadhyay
中科院分区：
文献类型：
--
作者：
P. Weichman;R. Mukhopadhyay
我们研究了粒子空穴对称性对各种量子相变的普遍性类的作用，这些相变对应于淬火随机介质中玻色子在零温度下超流性的开始。该问题在 d 空间维度上的函数积分公式产生了具有扩展无序的 (d+1) 维经典 XY 模型，即所谓的随机杆问题。然后可以通过添加非零位点能量来打破粒子孔对称性。我们可以区分三种情况：（i）精确的粒子空穴对称性，其中位点能量全部消失，（ii）统计粒子空穴对称性，其中位点能量分布关于零对称，平均消失，以及（iii）完全不存在粒子空穴对称性，其中分布是通用的。我们在每种情况下探索非超流体莫特绝缘相和玻色玻璃相中激发的性质。我们发现玻色玻璃可压缩性（解释了时间自旋刚度或超流体密度）在情况（ii）和（iii）中为正，但随着完全粒子空穴对称性的恢复，它会随着本质奇点而消失。然后，我们关注临界点并讨论类型 (ii) 粒子空穴对称性破缺扰动与随机杆临界行为的相关性。我们认为，类型 (iii) 的扰动与所得到的类型 (ii) 临界行为无关：统计对称性在接近临界点的大尺度上恢复，因此情况 (ii) 描述了脏玻色子不动点。为了研究更高的维度，我们尝试将 Dorogovtsev-Cardy-Boyanovsky 双 epsilon 展开技术推广到这个问题，并取得了部分成功。该技术提供的定性重整化群流程图非常引人注目。
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.