We present a unified framework for the renormalisation of the Hamiltonian and eigenbasis of a system of correlated electrons, unveiling thereby the interplay between electronic correlations and many-particle entanglement. For this, we extend substantially the unitary renormalization group (URG) scheme introduced in Refs. [1], [2], [3]. We recast the RG as a discrete flow of the Hamiltonian tensor network, i.e., the collection of various 2n-point scattering vertex tensors comprising the Hamiltonian. The renormalisation progresses via unitary transformations that block diagonalizes the Hamiltonian iteratively via the disentanglement of single-particle eigenstates. This procedure incorporates naturally the role of quantum fluctuations. The RG flow equations possess a non-trivial structure, displaying a feedback mechanism through frequency-dependent dynamical self-energies and correlation energies. The interplay between various UV energy scales enables the coupled RG equations to flow towards a stable fixed point in the IR. The effective Hamiltonian at the IR fixed point generically has a reduced parameter space, as well as number of degrees of freedom, compared to the microscopic Hamiltonian. Importantly, the vertex RG flows are observed to govern the RG flow of the tensor network that denotes the coefficients of the many-particle eigenstates. The RG evolution of various many-particle entanglement features of the eigenbasis are, in turn, quantified through the coefficient tensor network. In this way, we show that the URG framework provides a microscopic understanding of holographic renormalisation: the RG flow of the vertex tensor network generates a eigenstate coefficient tensor network possessing a many-particle entanglement metric. We find that the eigenstate tensor network accommodates sign factors arising from fermion exchanges, and that the IR fixed point reached generically involves a trivialisation of the fermion sign factor. Several results are presented for the emergence of composite excitations in the neighbourhood of a gapless Fermi surface, as well as for the condensation phenomenon involving the gapping of the Fermi surface.

我们为相关电子系统的哈密顿量和本征基重归一化提供了一个统一的框架，从而揭示了电子相关性与多粒子纠缠之间的相互作用。为此，我们充分扩展了参考文献中引入的单一重整化组（URG）方案。[1]，[2]，[3]。我们将RG重塑为哈密顿张量网络的离散流，即各种2 n的集合哈密​​顿量的点散射顶点张量。通过归一化变换进行重归一化，该变换通过单粒子本征态的解缠使块对角化哈密顿量。此过程自然包含了量子涨落的作用。RG流动方程具有非平凡的结构，通过依赖于频率的动态自能和相关能来显示反馈机制。各种紫外线能级之间的相互作用使耦合的RG方程能够向IR中的稳定固定点流动。与微观哈密顿量相比，IR不动点处的有效哈密顿量通常具有减少的参数空间以及自由度数。重要的，观察到顶点RG流控制张量网络的RG流，该张量网络表示多粒子本征态的系数。本征基的各种多粒子纠缠特征的RG演化又通过系数张量网络进行量化。这样，我们表明，URG框架提供了全息重新规范化的微观理解：顶点张量网络的RG流生成了具有多粒子纠缠度的本征态张量网络。我们发现，本征态张量网络容纳了由费米子交换引起的符号因子，并且达到的IR不动点通常涉及费米子符号因子的琐碎化。