Capturing the interplay between electronic correlations and many-particle entanglement requires a unified framework for Hamiltonian and eigenbasis renormalization. In this work, we apply the unitary renormalization group (URG) scheme developed in a companion work [1] to the study of two archetypal models of strongly correlated lattice electrons, one with translation invariance and one without. We obtain detailed insight into the emergence of various gapless and gapped phases of quantum electronic matter by computing effective Hamiltonians from numerical evaluation of the various RG equations, as well as their entanglement signatures through their respective tensor network descriptions. For the translationally invariant model of a single-band of interacting electrons, this includes results on gapless metallic phases such as the Fermi liquid and Marginal Fermi liquid, as well as gapped phases such as the reduced Bardeen-Cooper-Schrieffer, pair density-wave and Mott liquid phases. Additionally, a study of a generalised Sachdev-Ye model with disordered four-fermion interactions offers detailed results on many-body localised phases, as well as thermalised phase. We emphasise the distinctions between the various phases based on a combined analysis of their dynamical (obtained from the effective Hamiltonian) and entanglement properties. Importantly, the RG flow of the Hamiltonian vertex tensor network is shown to lead to emergent gauge theories for the gapped phases. Taken together with results on the holographic spacetime generated from the RG of the many-particle eigenstate (seen through, for instance, the holographic upper bound of the one-particle entanglement entropy), our analysis offer an ab-initio perspective of the gauge-gravity duality for quantum liquids that are emergent in systems of correlated electrons.

要捕获电子相关性和多粒子纠缠之间的相互作用，需要一个用于汉密尔顿和本征基重归一化的统一框架。在这项工作中，我们将在伴随工作[1]中开发的统一重整化组（URG）方案用于研究强相关晶格电子的两个原型模型，一个具有平移不变性，一个没有平移不变性。通过计算各种RG方程的数值计算以及它们各自的张量网络描述的纠缠签名，我们可以通过计算有效的哈密顿量，来详细了解量子电子物质的各种无间隙和带隙相的出现。对于单带相互作用电子的平移不变模型，这包括对无间隙金属相（例如费米液相和边际费米液相）以及带隙相（如还原的Bardeen-Cooper-Schrieffer，成对密度波和Mott液相）进行分析的结果。此外，对具有无序四费米子相互作用的广义Sachdev-Ye模型的研究提供了有关多体局部相和热化相的详细结果。我们基于对它们的动力学（从有效哈密顿量获得）和纠缠特性的综合分析，强调了各个相之间的区别。重要的是，哈密顿顶点张量网络的RG流显示出导致间隙相的涌现规范理论。与多粒子本征态RG产生的全息时空结果结合在一起（例如，通过