Related papers: Transfer matrix for spanning trees, webs and color…
We solve the classical square-lattice dimer model with periodic boundaries and in the presence of a field $\boldsymbol{t}$ that couples to the (vector) flux, by diagonalizing a modified version of Lieb's transfer matrix. After deriving the…
Jordan cells in transfer matrices of finite lattice models are a signature of the logarithmic character of the conformal field theories that appear in their thermodynamical limit. The transfer matrix of periodic loop models, T_N, is an…
The question of suitability of transfer matrix description of electrons traversing grating-type dielectric laser acceleration (DLA) structures is addressed. It is shown that although matrix considerations lead to interesting insights, the…
Working with Lieb's transfer matrix for the dimer model, we point out that the full set of dimer configurations may be partitioned into disjoint subsets (sectors) closed under the action of the transfer matrix. These sectors are labelled by…
The transfer matrix is a powerful technique that can be applied to statistical mechanics systems as, for example, in the calculus of the entropy of the ice model. One interesting way to study such systems is to map it onto a 3-color…
A transfer matrix method is presented for solving the scattering problem for the quasi one-dimensional massless Dirac equation applied to graphene in the presence of an arbitrary inhomogeneous electric and perpendicular magnetic field. It…
We introduce a general model of dimer coverings of certain plane bipartite graphs, which we call rail yard graphs (RYG). The transfer matrices used to compute the partition function are shown to be isomorphic to certain operators arising in…
The central charge of the dimer model on the square lattice is still being debated in the literature. In this paper, we provide evidence supporting the consistency of a $c=-2$ description. Using Lieb's transfer matrix and its description in…
We propose a new method to enumerate alternating knots using a transfer matrix approach. We apply it to count numerically various objects, including prime alternating tangles with two connected components, up to order 18--22, and comment on…
Transmission probabilities of Dirac fermions in graphene under linear barrier potential oscillating in time are investigated. Solving Dirac equation we end up with the solutions of the energy spectrum depending on several modes coming from…
We present a comprehensive and self-contained discussion of the use of the transfer matrix to study propagation in one-dimensional lossless systems, including a variety of examples, such as superlattices, photonic crystals, and optical…
A lattice model of critical dense polymers is solved exactly for arbitrary system size on the torus. More generally, an infinite family of lattice loop models is studied on the torus and related to the corresponding Fortuin-Kasteleyn random…
We introduce a transfer matrix method for the spectral analysis of discrete Hermitian operators with locally finite hopping. Such operators can be associated with a locally finite graph structure and the method works in principle on any…
Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law.…
We study the transport properties of Dirac fermions through gapped graphene through a magnetic barrier irradiated by a laser field oscillating in time. We use Floquet theory and the solution of Weber's differential equation to determine the…
We review a recently developed transfer matrix formulation of the stationary scattering in two and three dimensions where the transfer matrix is a linear operator acting in an infinite-dimensional function space. We discuss its utility in…
We show how to use the link representation of the transfer matrix $D_N$ of loop models on the lattice to calculate partition functions, at criticality, of the Fortuin-Kasteleyn model with various boundary conditions and parameter $\beta = 2…
A model is presented consisting of triangular trimers on the triangular lattice. In analogy to the dimer problem, these particles cover the lattice completely without overlap. The model has a honeycomb structure of hexagonal cells separated…
We propose a transfer matrix algorithm for the enumeration of alternating link diagrams with external legs, giving a weight $n$ to each connected component. Considering more general tetravalent diagrams with self-intersections and…
Data-driven reduced order models (ROMs) recently emerged as powerful tool for the solution of inverse scattering problems. The main drawback of this approach is that it was limited to the measurement arrays with reciprocally collocated…