论文标题
全息纠缠拓扑顺序在量子液体中
Holographic entanglement renormalisation of topological order in a quantum liquid
论文作者
论文摘要
我们介绍了一个新型的动量空间纠缠重新归一化组（MERG）方案，以使用未统一的量子电路组成非统一的量子电路，该方案在方格上（\ cite {anirbanmotti，anirbanmott2}）在方形晶格上的2D Hubbard模型的基态（T.O.）方案。在每个MERG步骤中，统一量子电路会驱散一组电子状态，从而改变了许多粒子状态的张量网络表示。通过将非本地统一门表示为两量形脱节门的乘积，我们为默格提供了纠缠全息图（EHM）表示。使用量子信息理论和复杂网络理论的基于纠缠的措施，我们研究了大部分EHM中拓扑顺序的出现。 MERG揭示了正常金属有序的绝缘液体和Neél抗磁磁性对称对称性的地面状态的明显全息纠缠特征，在参考文献中发现了半填充的2D Hubbard模型。参考文献中发现的孔掺杂的2D哈项模型的量子临界点的MERG分析揭示了量子液态基态的多个粒子纠缠的演变，并具有孔掺杂的量子液态，以及Mottness的崩溃以及D-Wave崩溃的崩溃是如何导致D-Wave超级导出的出现的。我们对EHM网络进行信息理论分析，表明信息瓶颈原理是EHM网络的继承结构中纠缠特征的蒸馏。结果，我们基于我们的EHM网络构建了深层神经网络（DNN）体系结构，并利用它来预测拓扑顺序的开始。我们还证明了DNN能够区分拓扑排序和无骨的正常金属相。
We introduce a novel momentum space entanglement renormalization group (MERG) scheme for the topologically ordered (T.O.) ground state of the 2D Hubbard model on a square lattice (\cite{anirbanmotti,anirbanmott2}) using a unitary quantum circuit comprised of non-local unitary gates. At each MERG step, the unitary quantum circuit disentangles a set of electronic states, thereby transforming the tensor network representation of the many-particle state. By representing the non-local unitary gate as a product of two-qubit disentangler gates, we provide an entanglement holographic mapping (EHM) representation for MERG. Using entanglement based measures from quantum information theory and complex network theory, we study the emergence of topological order in the bulk of the EHM. The MERG reveals distinct holographic entanglement features for the normal metallic, topologically ordered insulating quantum liquid and Neél antiferromagnetic symmetry-broken ground states of the 2D Hubbard model at half-filling found in Ref.\cite{anirbanmotti}. An MERG analysis of the quantum critical point of the hole-doped 2D Hubbard model found in Ref.\cite{anirbanmott2} reveals the evolution of the many-particle entanglement of the quantum liquid ground state with hole-doping, as well as how the collapse of Mottness is responsible for the emergence of d-wave superconductivity. We perform an information theoretic analysis of the EHM network, demonstrating that the information bottleneck principle is responsible for the distillation of entanglement features in the heirarchical structure of the EHM network. As a result, we construct a deep neural network (DNN) architecture based on our EHM network, and employ it for predicting the onset of topological order. We also demonstrate that the DNN is capable of distinguishing between the topologically ordered and gapless normal metallic phases.
