相关论文: Diagonalizing transfer matrices and matrix product…

Exact diagonalization is a well-established method for simulating small quantum systems. Its applicability is limited by the exponential growth of the so-called Hamiltonian matrix that needs to be diagonalized. Physical symmetries are…

This paper proposes a Newton-type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matrices are simultaneously diagonalizable. From a suitable…

We use the well-known isomorphism between operator algebras and function spaces equipped with a star product to study the asymptotic properties of certain matrix sequences in which the matrix dimension $D$ tends to infinity. Our approach is…

Complicated mathematical equations involving products of tensors with permutation symmetries, frequently encountered in fields such as general relativity and quantum chemistry (e.g., equations in high-order coupled cluster theories),…

Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their…

In this paper, some real-world motivated examples are provided illustrating the power of linear algebra tools as the product of matrices, determinants, eigenvalues and eigenvectors. In this sense, some practical applications related to…

The accuracy of different transfer matrix approaches, widely used to solve the stationary effective mass Schr\"{o}dinger equation for arbitrary one-dimensional potentials, is investigated analytically and numerically. Both the case of a…

In this paper, we introduce a particular class of matrices. We study the concept of a matrix to be \emph{balanced}. We study some properties of this concept in the context of matrix operations. We examine the behaviour of various matrix…

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…

The aim of this review paper is to discuss some applications of orthogonal polynomials in quantum information processing. The hope is to keep the paper self contained so that someone wanting a brief introduction to the theory of orthogonal…

In this paper, we define the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We…

The evolution of complex correlated quantum systems such as random circuit networks is governed by the dynamical buildup of both entanglement and entropy. We here introduce a real-time field theory approach -- essentially a fusion of the $G…

This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…

Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…

We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…

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…

A method is presented for fast diagonalization of a 2x2 or 3x3 real symmetric matrix, that is determination of its eigenvalues and eigenvectors. The Euler angles of the eigenvectors are computed. A small computer algebra program is used to…

In this paper we present a method for deriving effective one-dimensional models based on the matrix product state formalism. It exploits translational invariance to work directly in the thermodynamic limit. We show, how a representation of…

This paper presents iterative methods for solving tensor equations involving the T-product. The proposed approaches apply tensor computations without matrix construction. For each initial tensor, these algorithms solve related problems in a…

We propose a gradient-based Jacobi algorithm for a class of maximization problems on the unitary group, with a focus on approximate diagonalization of complex matrices and tensors by unitary transformations. We provide weak convergence…