Rigorous Free-Fermion Entanglement Renormalization from Wavelet Theory
Rigorous Free-Fermion Entanglement Renormalization from Wavelet Theory
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DOI：
10.1103/physrevx.8.011003
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发表时间：
2018-01-09
影响因子：
12.5
通讯作者：
Scholz, Volkher B.
中科院分区：
文献类型：
--
作者：
Haegeman, Jutho;Swingle, Brian;Scholz, Volkher B.
我们构造纠缠重整化方案，证明近似的基态的非相互作用费米子最近邻跳跃哈密顿的一维离散线和二维正方形晶格。这些方案给出了分层的量子电路，这些电路从非纠缠的自由度建立状态。该电路是基于对离散小波变换，这是近似相关的“半移位”：平移半个单位细胞。二维模型中费米面的存在需要一种特殊的电路结构来正确地捕获基态中的纠缠。我们展示了如何在近似误差可以控制，而无需进行变分优化。
We construct entanglement renormalization schemes that provably approximate the ground states of noninteracting-fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice. These schemes give hierarchical quantum circuits that build up the states from unentangled degrees of freedom. The circuits are based on pairs of discrete wavelet transforms, which are approximately related by a "half-shift": translation by half a unit cell. The presence of the Fermi surface in the two-dimensional model requires a special kind of circuit architecture to properly capture the entanglement in the ground state. We show how the error in the approximation can be controlled without ever performing a variational optimization.