Related papers: PairDiagSph: Generalization of the Exact Pairing D…
The accurate modeling of spin-orbit coupling (SOC) effects in diverse complex systems remains a significant challenge due to the high computational demands of density functional theory (DFT) and the limited transferability of existing…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
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…
The canonical quantum Hamiltonian eigenvalue problem for an anharmonic oscillator with a Lagrangian L = \dot{\phi}^2/2 - m^2 \phi^2/2 - g m^3 \phi^4 is numerically solved in two ways. One of the ways uses a plain cutoff on the number of…
Due to non-linear structure, iterative Green's function methods can result in multiple different solutions even for simple molecular systems. In contrast to the wave-function methods, a detailed and careful analysis of such molecular…
The exactly and quasi-exactly solvable problems for spin one-half in one dimension on the basis of a hidden dynamical symmetry algebra of Hamiltonian are discussed. We take the supergroup, $OSP(2|1)$, as such a symmetry. A number of exactly…
We present a new methodology to solve the Anderson impurity model, in the context of dynamical mean-field theory, based on the exact diagonalization method. We propose a strategy to effectively refine the exact diagonalization solver by…
Non-Hermitian systems exhibiting topological properties are attracting growing interest. In this work, we propose an algorithm for solving the ground state of a non-Hermitian system in the matrix product state (MPS) formalism based on a…
Computing ground states of local Hamiltonians is a fundamental problem in condensed matter physics. We give the first randomized polynomial-time algorithm for finding ground states of gapped one-dimensional Hamiltonians: it outputs an…
We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives…
. The choice of a suitable random matrix model of a complex system is very sensitive to the nature of its complexity. The statistical spectral analysis of various complex systems requires, therefore, a thorough probing of a wide range of…
We present a method for obtaining efficient probabilistic solutions to geostatistical and linear inverse problems in spherical geometry. Our Spherical Direct Sequential Simulation (SDSSIM) framework combines information from possibly noisy…
A complete classification of 2D superintegrable systems on two-dimensional conformally flat spaces has been performed over the years and 58 models, divided into 12 equivalence classes, have been obtained. We will re-examine two…
We present a suite of "holographic" quantum algorithms for efficient ground-state preparation and dynamical evolution of correlated spin-systems, which require far-fewer qubits than the number of spins being simulated. The algorithms…
We present a diagonalization method for generic matrix valued Hamiltonians based on a formal expansion in power of $\hbar $. Considering $\hbar $ as a running parameter, a differential equation connecting two diagonalization processes for…
We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of \"Ostlund…
The widely used large-scale diagonalization method using harmonic oscillator basis functions (an instance of the Rayleigh-Ritz method, also called a spectral method, configuration-interaction method, or ``exact diagonalization'' method) is…
We present Polfed$.$jl, an open-source Julia package implementing the Polynomially Filtered Exact Diagonalization (POLFED) algorithm for computing mid-spectrum eigenvalues and eigenvectors (shortly, eigenpairs) of quantum many-body…
A one-dimensional model of coupled spin-1/2 spins and pseudospin-1/2 orbitals with nearest-neighbor interaction is rigorously shown to exhibit spin-orbital separation by means of a non-local unitary transformation. On an open chain, this…
This work is a sequel to our work "The Spin Density Matrix I: General Theory and Exact Master Equations" (eprint arXiv:0708.0644 [cond-mat]). Here we compare pure- and pseudo-spin dynamics using as an example a system of two quantum dots, a…