Related papers: Renormalization Group and Quantum Information
Quantile normalisation is a popular normalisation method for data subject to unwanted variations such as images, speech, or genomic data. It applies a monotonic transformation to the feature values of each sample to ensure that after…
We introduce a picture to analyze the density matrix renormalization group (DMRG) numerical method from a quantum information perspective. This leads us to introduce some modifications for problems with periodic boundary conditions in which…
Given a renormalization scheme, we show how to formulate a tractable convex relaxation of the set of feasible local density matrices of a many-body quantum system. The relaxation is obtained by introducing a hierarchy of constraints between…
Low-energy effective theories have been used very successfully to study the low-energy limit of QCD, providing us with results for a plethora of phenomena, ranging from bound-state formation to phase transitions in QCD. These theories are…
The quantum field theory of two-dimensional sigma models with bulk and boundary couplings provides a natural framework to realize and unite different species of geometric flows that are of current interest in mathematics. In particular, the…
Based on the original idea of the density matrix renormalization group (DMRG), i.e. to include the missing boundary conditions between adjacent blocks of the blocked quantum system, we present a rigorous and nonperturbative mathematical…
The gravitational asymptotic safety program envisions a high-energy completion of the gravitational interactions by an interacting renormalization group fixed point, the Reuter fixed point. The primary tool for investigating this scenario…
We present an algorithm for the calculation of eigenstates with definite linear momentum in quantum lattices. Our method is related to the Density Matrix Renormalization Group, and makes use of the distribution of multipartite entanglement…
When working with quantum states, analysis of the final quantum state generated through probabilistic measurements is essential. This analysis is typically conducted by constructing the density matrix from either partial or full tomography…
We investigated the back reaction of cosmological perturbations on the evolution of the universe using the second order perturbation of the Einstein's equation. To incorporate the back reaction effect due to the inhomogeneity into the…
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory as well as number theory and…
Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…
We explore the implications of recent work by Br\'ezin and Zinn-Justin, applying the renormalization group techniques from critical phenomena to the scaling limit of matrix models in two-dimensional quantum gravity. They endeavor to get the…
We discuss some higher-loop studies of renormalization-group flows and fixed points in various quantum field theories.
Although substantial progress has been achieved in solving quantum impurity problems, the numerical renormalization group (NRG) method generally performs poorly when applied to quantum lattice systems in a real-space blocking form. The…
White's density matrix renormalization group ({DMRG}) method has been applied to the one-dimensional Ising model in a transverse field ({ITF}), in order to study the accuracy of the numerical algorithm. Due to the exact solubility of the…
The choice of the regularization scheme in Loop Quantum Cosmology (LQC) is crucial for the predicted phenomenology. We outline how the improved scheme can be naturally realized in Quantum Reduced Loop Gravity, describing the Universe as an…
The quantum gauge general relativity is proposed in the framework of quantum gauge theory of gravity. It is formulated based on gauge principle which states that the correct symmetry for gravitational interactions should be gravitational…
We review the asymptotic safety scenario for quantum gravity and the role and implications of an underlying ultraviolet fixed point. We discuss renormalisation group techniques employed in the fixed point search, analyse the main picture at…
The random matrix ensembles (RME), especially Gaussian random matrix ensembles GRME and Ginibre random matrix ensembles, are applied to following quantum systems: nuclear systems, molecular systems, and two-dimensional electron systems…