arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1503.05199cond-mat.str-el
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竞争秩序和反常现象

Competing Orders and Anomalies

Eun-Gook Moon

摘要:

守恒定律是自然界最基本的性质之一,但某些守恒“定律”可能会被内在的量子力学效应破坏,即所谓的量子反常。这些异常的深刻性质加深了我们对量子多体系统的理解。在这里,我们调查的量子相变之间的竞争订单和显着的后果,他们的存在量子反常效应。我们显式地计算了具有Wess-Zumino-Witten(WZW)项的非线性西格玛模型(NLSMs)反常的拓扑性质.非微扰的性质与特胡夫特反常匹配条件直接相关:反常在重整化群流中是守恒的。通过应用的匹配条件,我们表明,无质量的激发是强制执行的异常在整个相图中形成鲜明对比的情况下,只有大规模的激发在对称相位的Landau-Ginzburg-Wilson理论。此外,我们发现非微扰的标准来表征量子相变之间的竞争订单。例如,在4D中,我们展示了两个竞争的序参量理论,CP(1)和具有WZW的NLSM,描述了不同的普适类。讨论了这些反常现象的物理实现和实验意义。

英文摘要:

A conservation law is one of the most fundamental properties in nature, but a certain class of conservation "laws"' could be spoiled by intrinsic quantum mechanical effects, so-called quantum anomalies. Profound properties of the anomalies have deepened our understanding in quantum many body systems. Here, we investigate quantum anomaly effects in quantum phase transitions between competing orders and striking consequences of their presence. We explicitly calculate topological nature of anomalies of non-linear sigma models (NLSMs) with the Wess-Zumino-Witten (WZW) terms. The non-perturbative nature is directly related with the 't Hooft anomaly matching condition : anomalies are conserved in renormalization group flow. By applying the matching condition, we show massless excitations are enforced by the anomalies in a whole phase diagram in sharp contrast to the case of the Landau-Ginzburg-Wilson theory which only has massive excitations in symmetric phases. Furthermore, we find non-perturbative criteria to characterize quantum phase transitions between competing orders. For example, in 4D, we show the two competing order parameter theories, CP(1) and the NLSM with WZW, describe different universality class. Physical realizations and experimental implication of the anomalies are also discussed.

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