Highly Entangled Quantum Matter

在小学，我们被告知物质有四种状态：固体、液体、气体和等离子体。在大学里，我们了解到物质不止有四种状态。例如，磁化现象揭示了铁磁相的存在，零粘性现象揭示了超流相的存在。在我们的富裕世界中有如此多的相，令人惊讶的是，这些相能够被朗道的对称破缺理论系统地理解。但我们的世界更丰富，更令人惊叹。在这个提议中，我们将研究一类全新的量子物质，它超越了朗道对称破缺理论。我们将研究新的“拓扑”现象，它揭示了这些新相的存在--拓扑有序相。就像零粘性定义超流体秩序一样，新的“拓扑”现象定义了宏观层面的拓扑秩序。最近，我们发现，在微观水平上，拓扑有序是由长程量子纠缠引起的，就像费米子超流体是由费米子对凝聚引起的一样。长程量子纠缠导致了许多令人惊讶的涌现现象，如分数电荷、分数/非阿贝尔统计和理想的导电边缘通道。我们发现，长程量子纠缠(或拓扑有序)甚至可以提供光和电子的统一起源：光波是长程纠缠的涨落，电子是长程纠缠的缺陷。长程量子纠缠(以及相关的拓扑序)代表了凝聚态物理学的新篇章和未来发展方向，甚至是整个物理学的发展方向。

In primary school, we were told that there are four states of matter: solid, liquid, gas, and plasma. In college, we learned that there are much more then four states of matter. For example, the phenomenon of magnetization reveals the existence of ferromagnetic phases and the phenomenon of zero-viscosity reveals the existence of superfluid phases. There are so many phases in our rich world, and it is amazing that those phases can be understood systematically by the symmetry breaking theory of Landau. But our world is even richer and more amazing. In this proposal, we are going to study a totally new class of quantum matter that is beyond Landau symmetry breaking theory. We will study new "topological" phenomena that reveal the existence of those new phases -- topologically ordered phases. Just like zero-viscosity define the superfluid order, the new "topological" phenomena define the topological order at the macroscopic level. Recently, we found that, at the microscopical level, topological order is due to long-range quantum entanglements, just like fermion superfluid is due to fermion-pair condensation. Long-range quantum entanglements lead to many amazing emergent phenomena, such as fractional charges, fractional/non-Abelian statistics, and perfect conducting edge channels. We find that long-range quantum entanglements (or topological order) can even provide a unified origin of light and electrons: light waves are fluctuations of long-range entanglements, and electrons are defects of long-range entanglements. Long-range quantum entanglements (and the related topological order) represent a new chapter and a future direction of condensed matter physics, or even physics in general.