Related papers: Guide to Exact Diagonalization Study of Quantum Th…
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…
A theory of transformation is presented for the diagonalization of a Hamiltonian that is quadratic in creation and annihilation operators or in coordinates and momenta. It is the systemization and theorization of Dirac and…
We present a parallel computation scheme based on the Arnoldi algorithm for exact diagonalization of quantum-electron models. It contains a selective data transferring method and distributed storage format for efficient computing of the…
We study numerically a disordered transverse-field Ising Hamiltonian with long-range couplings. This model was recently investigated experimentally in a trapped-ion quantum simulator and was found to exhibit features of many-body…
We present a new math-physics modeling approach, called canonical quantization with numerical mode-decomposition, for capturing the physics of how incoming photons interact with finite-sized dispersive media, which is not describable by the…
The Eigenstate Thermalization Hypothesis explains thermalization in isolated quantum systems through the statistical properties of observables in the energy eigenbasis. We investigate the crossover from integrability to chaos in the…
Understanding quantum thermalization through entanglement build-up in isolated quantum systems addresses fundamental questions on how unitary dynamics connects to statistical physics. Here, we study the spin dynamics and approach towards…
Entanglement is the crucial ingredient of quantum many-body physics, and characterizing and quantifying entanglement in closed system dynamics of quantum simulators is an outstanding challenge in today's era of intermediate scale quantum…
We have studied the integer quantum Hall effect at finite temperatures by diagonalizing a single body tight binding model Hamiltonian including Aharonov-Bohm phase. We have studied the energy dependence of the specific heat and the Hall…
The thermalization phenomenon and many-body quantum statistical properties are studied on the example of several observables in isolated spin-chain systems, both integrable and generic non-integrable ones. While diagonal matrix elements for…
The determination of the energy spectra of small spin systems as for instance given by magnetic molecules is a demanding numerical problem. In this work we review numerical approaches to diagonalize the Heisenberg Hamiltonian that employ…
We present an exact diagonalization C++ template library (EDLib) for solving quantum electron models, including single-band finite Hubbard cluster and multi-orbital impurity Anderson model. The observables that can be computed using EDLib…
We provide a pedagogical introduction to eigenstate thermalization. This phenomenon, which occurs in generic quantum systems, allows one to understand why thermalization takes place in isolated systems under unitary dynamics. We motivate…
The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part…
A simple Mathematica code based on the differential realization of hard-core boson operators for finding exact solutions of the periodic-N spin-1/2 systems with or beyond nearest neighbor interactions is proposed, which can easily be used…
Exact diagonalization (ED) is an essential tool for exploring quantum many-body physics but is fundamentally limited by the exponentially-scaled computational complexity. Here, we propose tensor network variational diagonalization (TNVD),…
We describe a procedure to systematically improve direct diagonalization results for few-particle systems trapped in one-dimensional harmonic potentials interacting by contact interactions. We start from the two-body problem to define a…
An entirely quantum mechanical approach to diagonalize hermitean matrices has been presented recently. Here, the genuinely quantum mechanical approach is considered in detail for (2x2) matrices. The method is based on the measurement of…
Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a…
We present rigorous bounds on the thermalization time of the family of quantum mechanical spin systems known as stabilizer Hamiltonians. The thermalizing dynamics are modeled by a Davies master equation that arises from a weak local…