Related papers: Small parameter for lattice models with strong int…
A semi-analytic method to compute the first coefficients of the renormalization group functions on a random lattice is introduced. It is used to show that the two-dimensional $O(N)$ non-linear $\sigma$-model regularized on a random lattice…
The paper investigates localized deformation patterns resulting from the onset of instabilities in lattice structures. The study is motivated by previous observations on discrete hexagonal lattices, where the onset of non-uniform,…
We conjecture recurrence relations satisfied by the degrees of some linearizable lattice equations. This helps to prove linear growth of these equations. We then use these recurrences to search for lattice equations that have linear growth…
The problem of weakly correlated electrons on a square lattice is studied theoretically. A simple renormalization group scheme for the angle-resolved weight Z of the quasiparticles at the Fermi surface is presented and applied to the…
Constituent quark models, while successful, require a great deal of fine tuning of the short distance interactions by introducing phenomenological gluonic form factors which are ultimately designed to accurately reproduce the spectrum. We…
Resonant mode interactions in weakly nonlinear multi-dimensional lattices and related effects are described. We concentrate on formal description of the phenomenon and consider as examples mode interactions and evolution equations for…
We consider particles on a one-dimensional lattice whose evolution is governed by nearest-neighbor interactions where particles that have reached size zero are removed from the system. Concentrating on configurations with infinitely many…
Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…
We investigate a quasi-one dimensional system of trapped cold bosonic atoms in an optical lattice by using the density matrix renormalization group to study the Bose-Hubbard model at T=0 for experimentally realistic numbers of lattice…
We show that to understand the orthogonality catastrophe in the half-filled lattice model of spinless fermions with repulsive nearest neighbor interaction and a local impurity in its Luttinger liquid phase one has to take into account (i)…
A key starting assumption in many classical interatomic potential models for materials is a site energy decomposition of the potential energy surface into contributions that only depend on a small neighbourhood. Under a natural stability…
Nonlinear elastic metamaterials are known to support a variety of dynamic phenomena that enhance our capacity to manipulate elastic waves. Since these properties stem from complex, subwavelength geometry, full-scale dynamic simulations are…
The versatile technology of cold atoms confined in optical lattices allows the creation of a vast number of lattice geometries and interactions, providing a promising platform for emulating various lattice models. This opens the possibility…
Stability of recurrent models is closely linked with trainability, generalizability and in some applications, safety. Methods that train stable recurrent neural networks, however, do so at a significant cost to expressibility. We propose an…
In the first part of our theoretical study of correlated atomic wires on substrates, we introduced lattice models for a one-dimensional quantum wire on a three-dimensional substrate and their approximation by quasi-one-dimensional effective…
We study the real time evolution of the correlation functions in a globally quenched interacting one dimensional lattice system by means of time adaptive density matrix renormalization group. We find a clear light-cone behavior quenching…
The main technical and conceptual features of the lattice $1/N$ expansion in the scaling region are discussed in the context of a two-parameter two-dimensional spin model interpolating between $CP^{N-1}$ and $O(2N)$ $\sigma$ models, with…
Systems of identical particles possessing non-local interactions are capable of exhibiting extra-classical properties beyond the characteristic quantum length scales. This letter derives the dynamics of such systems in the non-relativistic…
The ground states of interacting one-dimensional metals are generically Luttinger liquids. Luttinger liquid theory is usually considered for translation invariant systems. The Luttinger liquid description remains valid for weak…
A short survey of the renormalization problem in QCD and its non-perturbative solution by means of numerical simulations on the lattice is given. Most emphasis is on scale dependent renormalizations, which can be reliably addressed via a…