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，我们学到了物质的四种状态。例如，磁化现象揭示了铁磁相的存在，零粘度现象揭示了超流相的存在。在我们这个丰富的世界里有如此多的相，令人惊奇的是，这些相可以用朗道的对称性破缺理论来系统地理解。但我们的世界更丰富，更令人惊叹。在这个提议中，我们将研究一种全新的量子物质，它超越了朗道对称性破缺理论。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。就像零粘性定义了超流秩序一样，新的“拓扑”现象定义了宏观层面的拓扑秩序。最近，我们发现，在微观层面上，拓扑有序是由于长程量子纠缠造成的，就像费米子超流体是由于费米子对凝聚造成的一样。长程量子纠缠导致了许多令人惊奇的涌现现象，例如分数电荷、分数/非阿贝尔统计和完美的导电边缘通道。我们发现，长程量子纠缠（或拓扑序）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（以及相关的拓扑秩序）代表了凝聚态物理学，甚至是一般物理学的新篇章和未来方向。

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.