Related papers: Coarse-graining renormalization by higher-order si…
Building upon previous $2D$ studies, this research focuses on describing $3D$ tensor renormalisation group (RG) flows for lattice spin systems, such as the Ising model. We present a novel RG map, which operates on tensors with…
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…
We have adjusted the Density Matrix Renormalization method to handle two dimensional systems of limited width. The key ingredient for this extension is the incorporation of symmetries in the method. The advantage of our approach is that we…
Identifying the relevant coarse-grained degrees of freedom in a complex physical system is a key stage in developing powerful effective theories in and out of equilibrium. The celebrated renormalization group provides a framework for this…
The anisotropic two-layer Ising model is studied by the phenomenological renormalizaiton group method. It is found that the anisotropic two-layer Ising model with symmetric couplings belongs to the same universality class as the two…
The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied for the first time to a model suffering the notorious quantum Monte Carlo sign problem --- the orbital $e_g$…
Recently a novel real-space RG algorithm was introduced, identifying the relevant degrees of freedom of a system by maximizing an information-theoretic quantity, the real-space mutual information (RSMI), with machine learning methods.…
We present the natural arguments for the rationality of a recently proposed simple approach for renormalization which is based solving differential equations. The renormalization group equation is also derived in a natural way and…
We present a method for contracting a square-lattice tensor network in two dimensions, based on auxiliary tensors accomplishing successive truncations (renormalization) of 8-index tensors for 2 by 2 plaquettes into 4-index tensors. The…
We present two approaches for coarse-graining interplanar potentials and determining the corresponding macroscopic cohesive laws based on energy relaxation and the renormalization group. We analyze the cohesive behavior of a large---but…
Real Space Renormalization Group (RSRG) treatment of Ising model for square and simple cubic lattice is investigated and critical coupling strengths of these lattices are obtained. The mathematical complications, which appear inevitable in…
A method for computing low--temperature series for renormalized operators in the two--dimensional Ising model is proposed. These series are applied to the study of the properties of the truncated renormalized Hamiltonians when we start at…
Inspired by the superblock method of White, we introduce a simple modification of the standard Renormalization Group (RG) technique for the study of quantum lattice systems. Our method which takes into account the effect of Boundary…
It is often assumed that for treating numerical (or experimental) data on continuous transitions the formal analysis derived from the Renormalization Group Theory can only be applied over a narrow temperature range, the "critical region";…
We present a new algorithm to calculate the thermodynamic quantities of three-dimensional (3D) classical statistical systems, based on the ideas of the tensor product state and the density matrix renormalization group. We represent the…
We propose an improved tensor renormalization group (TRG) algorithm, the bond-weighted TRG (BTRG). In BTRG, we generalize the conventional TRG by introducing bond weights on the edges of the tensor network. We show that BTRG outperforms the…
Real-space renormalization-group techniques for quantum systems can be divided into two basic categories - those capable of representing correlations following a simple boundary (or area) law, and those which are not. I discuss the scaling…
A variant of White's density matrix renormalisation group scheme which is designed to compute low-lying energies of one-dimensional quantum lattice models with a large number of degrees of freedom per site is described. The method is tested…
For scalar QED on a three-dimensional toroidal lattice with a fine lattice spacing we consider the renormalization problem of choosing counter terms depending on the lattice spacing, so that the theory stays finite as the spacing goes to…
Using the strong disorder renormalization group method we study numerically the critical behavior of the random transverse Ising model at a free surface, at a corner and at an edge in D=2, 3 and 4-dimensional lattices. The surface…