Related papers: Diagonalizing transfer matrices and matrix product…
The study of tensor network theory is an important field and promises a wide range of experimental and quantum information theoretical applications. Matrix product state is the most well-known example of tensor network states, which…
The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum…
The method of choice to study one-dimensional strongly interacting many body quantum systems is based on matrix product states and operators. Such method allows to explore the most relevant, and numerically manageable, portion of an…
We review some of the recent developments in two dimensional statistical mechanics in which corner transfer matrices provide the vital link between the physical system and the representation theory of quantum affine algebras. This opens…
This note deals with a simultaneous approximation of several matrices by a finite family of diagonalizable matrices satisfying an additional condition for the spectrum of a matrix product. That is the simplicity of all eigenvalues.
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…
The current paper presents a new approach to multilinear dynamical systems analysis and control. The approach is based upon recent developments in tensor decompositions and a newly defined algebra of circulants. In particular, it is shown…
We study a uniform matrix product state as a variational state for classical and quantum spin chains in the thermodynamic limit. Under a careful treatment of the translational symmetry, eigen values of the transfer matrix defined in the…
Matrix product states play an important role in quantum information theory to represent states of many-body systems. They can be seen as low-dimensional subvarieties of a high-dimensional tensor space. In these notes, we consider two…
Equiangular Algorithm generates a set of equiangular normalized vectors with given angle {\theta} using a set of linearly independence vectors in a real inner product space, which span the same subspaces. The outcome of EA on column vectors…
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
Products of random transfer matrices are applied to low dimensional disordered systems to evaluate numerically extensive quantities such as entropy and overlap probability distribution. The main advantage is the possibility to avoid…
We develop in full detail the formalism of tangent states to the manifold of matrix product states, and show how they naturally appear in studying time-evolution, excitations and spectral functions. We focus on the case of systems with…
The contraction of tensor networks is a central task in the application of tensor network methods to the study of quantum and classical many body systems. In this paper, we investigate the impact of gauge degrees of freedom in the virtual…
Neat stuff about eigenfunctions, transfer matrices, and a.c. spectrum of one-dimensional Schrodinger operators
The diagonalization of matrices may be the top priority in the application of modern physics. In this paper, we numerically demonstrate that, for real symmetric random matrices with non-positive off-diagonal elements, a universal scaling…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…
We introduce and extend the outer product and contractive product of tensors and matrices, and present some identities in terms of these products. We offer tensor expressions of derivatives of tensors, focus on the tensor forms of…
Analysis of ac electrical systems can be performed via frame transformations in the time-domain or via harmonic transfer functions (HTFs) in the frequency-domain. The two approaches each have unique advantages but are hard to reconcile…