Related papers: Numerical Renormalization Group at Criticality
The density matrix renormalization group is one of the most powerful numerical methods for computing ground-state properties of two-dimensional (2D) quantum lattice systems. Here we show its finite-temperature extensions are also viable for…
In this paper we propose a novel method to study critical systems numerically by a combined collective-mode algorithm and Renormalization Group on the lattice. This method is an improved version of MCRG in the sense that it has all the…
Different phenomenological RG transformations based on scaling relations for the derivatives of the inverse correlation length and singular part of the free-energy density are considered. These transformations are tested on the 2D square…
We present real--space renormalization group (RG) calculations of the critical properties of the random--field Ising model on a cubic lattice in three dimensions. We calculate the RG flows in a two--parameter truncation of the Hamiltonian…
We report current progress on the synthesis of methods to alleviate two major difficulties in implementing a Monte Carlo Renormalization Group (MCRG) for quantum systems. In particular, we have utilized the loop-algorithm to reduce critical…
We reformulate the density matrix renormalization group method (DMRG) in terms of a single block, instead of the standard left and right blocks used in the construction of the superblock. This version of the DMRG, which we call the puncture…
We develop a density matrix renormalization group (DMRG) algorithm for constrained quantum lattice models that successfully {\it{implements the local constraints as symmetries in the contraction of the matrix product states and matrix…
The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and…
We combine histogram reweighting techniques with the two-lattice matching Monte Carlo renormalization group method to conduct computationally efficient calculations of critical exponents on systems with moderately small lattice sizes. The…
A new density matrix renormalisation group (DMRG) approach is presented for quantum systems of two spatial dimensions. In particular, it is shown that it is possible to create a multi-chain-type 2D DMRG approach which utilises previously…
Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the finite size scaling hypothesis, the approximate…
The numerical renormalization group method is used to investigate zero temperature phase transitions in quantum impurity systems, in particular in the particle-hole symmetric soft-gap Anderson model. The model displays two stable phases…
We summarize our recent results on the large N renormalization group (RG) approach to matrix models for discretized two-dimensional quantum gravity. We derive exact RG equations by solving the reparametrization identities, which reduce…
Matrix models of 2D quantum gravity are either exactly solvable for matter of central charge $ c\leq 1, $ or not understood. It would be useful to devise an approximate scheme which would be reasonable for the known cases and could be…
We propose a scheme to perform tensor network based finite-size scaling analysis for two-dimensional classical models. In the tensor network representation of the partition function, we use higher-order tensor renormalization group (HOTRG)…
We propose a numerical self-consistent method for 3D classical lattice models, which optimizes the variational state written as two-dimensional product of tensors. The variational partition function is calculated by the corner transfer…
We investigate the entanglement spectrum in HOTRG ---tensor renormalization group (RG) method combined with the higher order singular value decomposition--- for two-dimensional (2D) classical vertex models. In the off-critical region, it is…
We introduce a general method for optimizing real-space renormalization-group transformations to study the critical properties of a classical system. The scheme is based on minimizing the Kullback-Leibler divergence between the distribution…
We consider the two-dimensional classical XY model on a square lattice in the thermodynamic limit using tensor renormalization group and precisely determine the critical temperature corresponding to the Berezinskii-Kosterlitz-Thouless (BKT)…
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…