Related papers: Renormalization group transformations on quantum s…
We study the quantum groups appearing via models $C(G)\subset M_K(C(X))$ which are "stationary", in the sense that the Haar integration over $G$ is the functional $tr\otimes\int_X$. Our results include a number of generalities, notably with…
The renormalization group is not only a powerful method for describing universal properties of phase transitions but it is also useful for evaluating non- universal properties beyond mean-field theory. In this contribution we concentrate on…
We introduce a simple instance of the renormalization group transformation in the Banach space of probability densities. By changing the scaling of the renormalized variables we obtain, as fixed points of the transformation, the L\'evy…
Renormalization group ideas and effective operators are used to efficiently determine localized unitaries for preparing the ground states of non-interacting scalar field theories on digital quantum devices. With these methods, classically…
The q-state ferromagnetic Potts model under a non-zero magnetic field coupled with the 0^th Potts state was investigated by an exact real-space renormalization group approach. The model was defined on a family of diamond hierarchical…
We introduce a real-space exact renormalization group method to find exactly solvable quantum spin chains and their ground states. This method allows us to provide a complete list for exact solutions within SU(2) symmetric quantum spin…
We apply the renormalization group theory to the dynamical systems with the simplest example of basic biological motifs. This includes the interpretation of complex networks as the perturbation to simple network. This is the first step to…
The renormalization group method has been adapted to the analysis of the long-time behavior of non-linear partial differential equation and has demonstrated its power in the study of critical phenomena of gravitational collapse. In the…
We introduce a way of implementing Wilson renormalization within the context of the theory of effective Hamiltonians. Our renormalization scheme involves manipulations at the level of the generalized $G$--matrix and is independent of any…
We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In…
In this paper we give an introduction to the numerical density matrix renormalization group (DMRG) algorithm, from the perspective of the more general matrix product state (MPS) formulation. We cover in detail the differences between the…
We analyse approximate solutions to an exact renormalisation group equation with particular emphasis on their dependence on the regularisation scheme, which is kept arbitrary. Physical quantities related to the coarse-grained potential of…
The ground-state and low-energy excitations of quantum Hall systems are studied by the density matrix renormalization group (DMRG) method. From the ground-state pair correlation functions and low-energy excitions, the ground-state phase…
We propose a method, based on matrix product states, for studying the time evolution of many-body quantum lattice systems under continuous and site-resolved measurement. Both the frequency and the strength of generalized measurements can be…
The Renormalisation Group (RG) is a systematic procedure used to regularise divergences appearing as artefacts when constructing solutions to a large class of differential problems, whether perturbatively or not. This paper is devoted to…
We review some of our recent results concerning the relationship between the Real-Space Renormalization Group method and Quantum Groups. We show this relation by applying real-space RG methods to study two quantum group invariant…
Phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method. A general formula for phase diffusion coefficients is…
A perturbative renormalization group method is used to obtain steady-state density profiles of a particle non-conserving asymmetric simple exclusion process. This method allows us to obtain a globally valid solution for the density profile…
We consider the most general scale invariant radial Hamiltonian allowing for anisotropic scaling between space and time. We formulate a renormalisation group analysis of this system and demonstrate the existence of a quantum phase…
Nanoscale topological spin textures in magnetic systems are emerging as promising candidates for scalable quantum architectures. Despite their potential as qubits, previous studies have been limited to semiclassical approaches, leaving a…