Related papers: Series expansions from the corner transfer matrix …
In the beginning of the 1970's, Wilson developed the concept of a fully non-perturbative renormalization group transformation. Applied to the Kondo problem, this numerical renormalization group method (NRG) gave for the first time the full…
We present a new and general method of weighted least square univariate regression where the dependent variable is expanded as a series of suitably chosen functions of the independent variables. Each term of the series is obtained by an…
The finite lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the spin-1 Ising model on the square lattice. A new formalism is described that…
In this paper we explore the practical use of the corner transfer matrix and its higher-dimensional generalization, the corner tensor, to develop tensor network algorithms for the classical simulation of quantum lattice systems of infinite…
We present a method to accelerate the numerical evaluation of spatial integrals of Feynman diagrams when expressed on the real frequency axis. This can be realized through use of a renormalized perturbation expansion with a constant but…
A novel method of summation for power series is developed. The method is based on the self-similar approximation theory. The trick employed is in transforming, first, a series expansion into a product expansion and in applying the…
In the Super-Transition-Array statistical method for the computation of radiative opacity of hot dense matter, the moments of the absorption or emission features involve partition functions with reduced degeneracies, occurring through the…
We introduce a numerical method to study critical properties near classical and quantum phase transitions. Our method applies ideas of the Tensor Renormalization Group to obtain an improved action which is used to extract critical…
Using the corner-transfer matrix renormalization group to contract the tensor network that describes its partition function, we investigate the nature of the phase transitions of the hard-square model, one of the exactly solved models of…
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is…
We introduce the order-separated Grassmann higher-order tensor renormalization group (OS-GHOTRG) method for QCD with staggered quarks in the strong-coupling expansion. The method allows us to determine the expansion coefficients of the…
We formulate a method of performing non-perturbative calculations in quantum field theory, based upon a derivative expansion of the exact renormalization group. We then proceed to apply this method to the calculation of critical exponents…
Structured reconstruction is a non-trivial dense prediction problem, which extracts structural information (\eg, building corners and edges) from a raster image, then reconstructs it to a 2D planar graph accordingly. Compared with common…
We use functional methods to compute one-loop effects in Heavy Quark Effective Theory. The covariant derivative expansion technique facilitates the efficient extraction of matching coefficients and renormalization group evolution equations.…
The behavior of dimensionless quantities defined as ratios of partition functions is analyzed to investigate phase transitions and critical phenomena. At criticality, the universal values of these ratios can be predicted from conformal…
Tensor networks (TNs) have become one of the most essential building blocks for various fields of theoretical physics such as condensed matter theory, statistical mechanics, quantum information, and quantum gravity. This review provides a…
There are many time series in the literature with high dimension yet limited sample sizes, such as macroeconomic variables, and it is almost impossible to obtain efficient estimation and accurate prediction by using the corresponding…
The density-matrix renormalization group (DMRG) applied to transfer matrices allows it to calculate static as well as dynamical properties of one-dimensional quantum systems at finite temperature in the thermodynamic limit. To this end the…
We introduce a versatile and practical framework for applying matrix product state techniques to continuous quantum systems. We divide space into multiple segments and generate continuous basis functions for the many-body state in each…
Tensor renormalization group, originally devised as a numerical technique, is emerging as a rigorous analytical framework for studying lattice models in statistical physics. Here we introduce a new renormalization map - the 2x1 map - which…