Related papers: Entanglement renormalization for disordered system…

We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering renormalization (TEFR) approach that…

Simulating the dynamics of quantum many-body systems with disorder is a fundamental challenge. In this work, we propose a general approach -- the statistics-encoded tensor network (SeTN) -- to study such systems. By encoding disorder into…

We examine the onset of Anderson localization in three-dimensional systems with structural disorder in the form of lattice irregularities and in the absence of any on-site disordered potential. Analyzing two models with distinct types of…

We develop a renormalization group method to investigate synchronization clusters in a one-dimensional chain of nearest-neighbor coupled phase oscillators. The method is best suited for chains with strong disorder in the intrinsic…

We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…

Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the…

In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensor-network states. The computational cost of…

Despite their high accuracy, complex neural networks demand significant computational resources, posing challenges for deployment on resource constrained devices such as mobile phones and embedded systems. Compression algorithms have been…

Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…

Deep networks can be trained to map images into a low-dimensional latent space. In many cases, different images in a collection are articulated versions of one another; for example, same object with different lighting, background, or pose.…

This study investigates the entanglement properties of disordered free fermion systems undergoing an Anderson phase transition from a delocalized to a localized phase. The entanglement entropy is employed to quantify the degree of…

We propose a method to compute the entanglement entropy (EE) using the tensor renormalization group (TRG) method. The reduced density matrix of a $d$-dimensional quantum system is represented as a $(d+1)$-dimensional tensor network. We…

We develop a new methodology to contract tensor networks within the corner transfer matrix renormalization group approach for a wide range of two-dimensional lattice geometries. We discuss contraction algorithms on the example of…

This work targets the influence of disorder on the relaxed structure and macroscopic mechanical properties of elastic networks. We construct network classes of different types of disorder (length, topology and stiffness), which are…

Motivated by long-range dispersal in ecological systems, we formulate and apply a general strong-disorder renormalization group (SDRG) framework to describe one-dimensional disordered contact processes with heavy-tailed, such as power law,…

We propose aNETT (augmented NETwork Tikhonov) regularization as a novel data-driven reconstruction framework for solving inverse problems. An encoder-decoder type network defines a regularizer consisting of a penalty term that enforces…

Previous work proposed a strong-disorder renormalization approach for the Anderson model, using it to calculate the density of states and the inverse participation ratio [Johri \& Bhatt, Phys.\ Rev.\ B {\bf 90} 060205(R) (2014)]. This is…

In this paper we review basic and emerging models and associated algorithms for large-scale tensor networks, especially Tensor Train (TT) decompositions using novel mathematical and graphical representations. We discus the concept of…

We derive an analytical density functional for the single-site entanglement of the one-dimensional homogeneous Hubbard model, by means of an approximation to the linear entropy. We show that this very simple density functional reproduces…

Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered…