论文标题
Kitaev Honeycomb模型的地面和激发状态的限制性玻尔兹曼机器表示
Restricted Boltzmann machine representation for the groundstate and excited states of Kitaev Honeycomb model
论文作者
论文摘要
在这项工作中，研究了限制性玻尔兹曼机器（RBMS）找到具有周期性边界条件的Kitaev Honeycomb模型的解决方案。比较了系统的测量地面（GS）能量，对于小晶格尺寸（例如$ 3 \ tims 3 $，带有$ 18 $旋转器），显示出与能量的分析价值相一致，高于$ 0.09 \％$。此外，我们发现的波浪函数具有$ 99.89 \％$的重叠，并具有确切的基态波函数。此外，讨论了在RBM中实现任何人的可能性，并给出了一种算法来构建这些任何一个任何兴奋，并将其编织为量子计算中可能的未来应用。使用（2+1）D和2D CFT中的拓扑字段理论之间的对应关系，我们提出了摩尔阅读状态和$ 2 $ d ISING模型中的RBM状态之间的识别。
In this work, the capability of restricted Boltzmann machines (RBMs) to find solutions for the Kitaev honeycomb model with periodic boundary conditions is investigated. The measured groundstate (GS) energy of the system is compared and, for small lattice sizes (e.g. $3 \times 3$ with $18$ spinors), shown to agree with the analytically derived value of the energy up to a deviation of $0.09\%$. Moreover, the wave-functions we find have $99.89\%$ overlap with the exact ground state wave-functions. Furthermore, the possibility of realizing anyons in the RBM is discussed and an algorithm is given to build these anyonic excitations and braid them for possible future applications in quantum computation. Using the correspondence between topological field theories in (2+1)d and 2d CFTs, we propose an identification between our RBM states with the Moore-Read state and conformal blocks of the $2$d Ising model.
