Related papers: Renormalization group method for weakly coupled qu…
We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of…
We aim at an explicit characterization of the renormalized Hamiltonian after decimation transformation of a one-dimensional Ising-type Hamiltonian with a nearest-neighbor interaction and a magnetic field term. To facilitate a deeper…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
The renormalization-group method is used to analyze the low-temperature behaviour of a two-dimentional, spin-$s$ quantum Heisenberg ferromagnet. A set of recursion equations is derived in an one-loop approximation. The low-temperature…
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…
We discuss the application of the method of characteristics to the renormalization-group equation for the perturbative QCD series within the electron-positron annihilation cross-section. We demonstrate how one such renormalization-group…
Numerous correlated electron systems exhibit a strongly scale-dependent behavior. Upon lowering the energy scale, collective phenomena, bound states, and new effective degrees of freedom emerge. Typical examples include (i) competing…
We present a simple proof of the all-order exponentiation of soft logarithmic corrections to hard processes in perturbative QCD. Our argument is based on proving that all large logs in the soft limit can be expressed in terms of a single…
We extend the density matrix renormalization group to compute exact ground states of continuum many-electron systems in one dimension with long-range interactions. We find the exact ground state of a chain of 100 strongly correlated…
I give an outline of recent applications of the renormalisation group to effective theories of nuclear forces, focussing on the use of a Wilsonian approach to analyse systems of two or three nonrelativistic particles.
In this Letter, we use a general renormalization-group algorithm to implement Propp and Wilson's "coupling from the past" approach to complex physical systems. Our algorithm follows the evolution of the entire configuration space under the…
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 analyze classical dimer models on the square and triangular lattice using a tensor network representation of the dimers. The correlation functions are numerically calculated using the recently developed "Tensor renormalization group"…
We analyze a semi-infinite one-dimensional random walk process with a biased motion that is incremental in one direction and long-range in the other. On a network with a fixed hierarchy of long-range jumps, we find with exact…
A new method of diagonalisation of the XY-Hamiltonian of inhomogeneous open linear chains with periodic (in space) changing Larmor frequencies and coupling constants is developed. As an example of application, multiple quantum dynamics of…
Quantum field theories require a cutoff to regulate divergences that result from local interactions, and yet physical results can not depend on the value of this cutoff. The renormalization group employs a transformation that changes the…
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…
The approximate joint diagonalization of a set of matrices consists in finding a basis in which these matrices are as diagonal as possible. This problem naturally appears in several statistical learning tasks such as blind signal…
We revisit Fradkin and Raby's real-space renormalization-group method to study the quantum Z_2 gauge theory defined on links forming a two-dimensional square lattice. Following an old suggestion of theirs, a systematic perturbation…
A linearized tensor renormalization group (LTRG) algorithm is proposed to calculate the thermodynamic properties of one-dimensional quantum lattice models, that is incorporated with the infinite time-evolving block decimation technique, and…