Related papers: Unitary Networks from the Exact Renormalization of…
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…
We set up the Functional Renormalisation Group formalism for Tensorial Group Field Theory in full generality. We then apply it to a rank-3 model over U(1) x U(1) x U(1), endowed with a linear kinetic term and nonlocal interactions. The…
In AdS/CFT, observables on the boundary are invariant under renormalization group (RG) flow in the bulk. In this paper, we study holographic entanglement entropy under bulk RG flow and find that it is indeed invariant. We focus on…
We study the phase diagram of the half-filled one-dimensional extended Hubbard model at weak coupling using a novel functional renormalization group (FRG) approach. The FRG method includes in a systematic manner the effects of the…
Central to the AdS/CFT correspondence is a precise relationship between the curvature of an anti-de Sitter (AdS) spacetime and the central charge of the dual conformal field theory (CFT) on its boundary. Our work shows that such a…
We investigate how the Unitary Correlation Operator Method (UCOM), developed to explicitly describe the strong short-range central and tensor correlations present in the nuclear many-body system, relates to the Similarity Renormalization…
The gradient flow exact renormalization group (GFERG) is a variant of the exact renormalization group (ERG) for gauge theory that is aimed at preserve gauge invariance as manifestly as possible. It achieves this goal by utilizing the…
We use TensorNetwork [C. Roberts et al., arXiv: 1905.01330], a recently developed API for performing tensor network contractions using accelerated backends such as TensorFlow, to implement an optimization algorithm for the Multi-scale…
We investigate how the holographic correspondence can be reformulated as a generalisation of Wilsonian RG flow in a strongly interacting large $N$ quantum field theory. We firstly define a \textit{highly efficient RG flow} as one in which…
Ensemble models of graphs are one of the most important theoretical tools to study complex networks. Among them, exponential random graphs (ERGs) have proven to be very useful in the analysis of social networks. In this paper we develop a…
Novel randomness-induced disordered ground states in two-dimensional (2D) quantum spin systems have been attracting much interest. For quantitative analysis of such random quantum spin systems, one of the most promising numerical approaches…
The density matrix renormalization group (DMRG) method generates the low-energy states of linear systems of $N$ sites with a few degrees of freedom at each site by starting with a small system and adding sites step by step while keeping…
A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi…
In this thesis, we present a novel method combining energy-based finite-size scaling with tensor network renormalization (TNR) to study phase transitions in lattice models. This approach effectively calculates running coupling constants and…
I derive a family of Ryu--Takayanagi formulae that are valid in the large $N$ limit of holographic quantum error-correcting codes, and parameterized by a choice of UV cutoff in the bulk. The bulk entropy terms are matched with a family of…
In the paper [Angelini M C, Parisi G, and Ricci-Tersenghi F, Ensemble renormalization group for disordered systems, Phys. Rev. B 87 134201 (2013)] we introduced a real-space renormalization group called Ensemble Renormalization Group (ERG)…
The study of probabilistic models for the analysis of complex networks represents a flourishing research field. Among the former, Exponential Random Graphs (ERGs) have gained increasing attention over the years. So far, only linear ERGs…
By combining the Grassmann algebra with multi-scale entanglement renormalization ansatz (MERA), we introduce a new unbiased and effective numerical method for simulating 2D strongly correlated electronic systems. The new GMERA method…
Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many interesting structural features of the AdS/CFT…
We analyze the renormalization-group (RG) flows of two effective Lagrangians, one for measurement induced transitions of monitored quantum systems and one for entanglement transitions in random tensor networks. These Lagrangians, previously…