相关论文: An Example of Symmetry Exploitation for Energy-rel…

A simple tight-binding model is used to illustrate how the time dependence of a state vector can be obtained from all the eigenvalues and eigenvectors of the Hamiltonian. The behavior of the eigenvalues and eigenvectors is studied for…

Domain specific localization of eigenstates has been a persistent observation for systems with local symmetries. The underlying mechanism for this localization behaviour has however remained elusive. We provide here an analysis of locally…

Ensuring a satisfactory statistical convergence of anharmonic thermodynamic properties requires sampling of many atomic configurations, however the methods to obtain those necessarily produce correlated samples, thereby reducing the…

Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…

An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The…

We study the entanglement Hamiltonian for free-fermion chains with a particular form of inhomogeneity. The hopping amplitudes and chemical potentials are chosen such that the single-particle eigenstates are related to discrete orthogonal…

Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…

A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…

We present broadly applicable tools for determining the behavior of eigenvalues and eigenvectors under the addition of self-adjoint operators and under the multiplication of unitaries, in finite-dimensional Hilbert spaces. The new tools…

The so-called equation of motion method is useful to obtain the explicit form of the eigenvectors and eigenvalues of certain non self-adjoint bosonic Hamiltonians with real eigenvalues. These operators can be diagonalized when they are…

The projection of the eigenfunctions obtained in standard plane-wave first-principle electronic-structure calculations into atomic-orbital basis sets is proposed as a formal and practical link between the methods based on plane waves and…

A common challenge faced in quantum physics is finding the extremal eigenvalues and eigenvectors of a Hamiltonian matrix in a vector space so large that linear algebra operations on general vectors are not possible. There are numerous…

We propose a general framework to study the stability of the subspace spanned by $P$ consecutive eigenvectors of a generic symmetric matrix ${\bf H}_0$, when a small perturbation is added. This problem is relevant in various contexts,…

Symmetry considerations are at the core of the major frameworks used to provide an effective mathematical representation of atomic configurations that is then used in machine-learning models to predict the properties associated with each…

We present a scheme to controllably improve the accuracy of tight-binding Hamiltonian matrices derived by projecting the solutions of plane-wave ab initio calculations on atomic orbital basis sets. By systematically increasing the…

We show that metamaterials can be used as a testing ground to investigate spontaneous symmetry breaking associated with non-Hermitian quantum systems. By exploring the interplay between near-field dipolar coupling and material absorption or…

We develop an algebraic approach for finding the eigenfunctions of a large class of few and many-body Hamiltonians, in one and higher dimensions, having linear spectra. The method presented enables one to exactly map these interacting…

It is shown that the eigenproblem of any $2\times 2$ matrix Hamiltonian with discrete eigenvalues is involved with a supersymmetric quantum mechanics. The energy dependence of the superalgebra marks the disparity between the deduced…

For nonrelativistic Hamiltonians which are shape invariant, analytic expressions for the eigenvalues and eigenvectors can be derived using the well known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess…

The Eigendecomposition of quadratic forms (symmetric matrices) guaranteed by the spectral theorem is a foundational result in applied mathematics. Motivated by a shared structure found in inferential problems of recent interest---namely…