Highly Entangled Quantum Matter

小学时，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，我们学过物质不止有四种状态。例如，磁化现象表明铁磁相的存在，零粘度现象表明超流相的存在。在我们这个富裕的世界里有如此多的相，这些相可以被朗道的对称性破缺理论系统地理解，这是令人惊讶的。但我们的世界更丰富，更神奇。在这个提议中，我们将研究一种全新的量子物质，它超越了朗道对称破缺理论。我们将研究新的“拓扑”现象，揭示这些新相的存在——拓扑有序相。就像零粘度定义了超流体秩序一样，新的“拓扑”现象在宏观水平上定义了拓扑秩序。最近，我们发现，在微观层面上，拓扑秩序是由于远程量子纠缠，就像费米子超流体是由于费米子对凝聚。长程量子纠缠导致了许多惊人的涌现现象，如分数电荷、分数/非阿贝尔统计和完美的导电边缘通道。我们发现，远程量子纠缠（或拓扑秩序）甚至可以提供光和电子的统一起源：光波是远程纠缠的涨落，电子是远程纠缠的缺陷。远程量子纠缠（以及相关的拓扑顺序）代表了凝聚态物理学的新篇章和未来方向，甚至是一般物理学。

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.