Related papers: PairDiagSph: Generalization of the Exact Pairing D…
We present a program for solving exactly the general pairing Hamiltonian based on diagonalization. The program generates the seniority-zero shell-model-like basis vectors via the `01' inversion algorithm. The Hamiltonian matrix is…
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…
We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a…
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…
There has been increasing interest in studying the Richardson model from which one can derive the exact solution for certain pairing Hamiltonians. However, it is still a numerical challenge to solve the nonlinear equations involved. In this…
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…
Spin models like the Heisenberg Hamiltonian effectively describe the interactions of open-shell transition-metal ions on a lattice and can account for various properties of magnetic solids and molecules. Numerical methods are usually…
Exact diagonalization and other numerical studies of quantum spin systems are notoriously limited by the exponential growth of the Hilbert space dimension with system size. A common and well-known practice to reduce this increasing…
We present a numerical method based on real-space renormalization that outputs the exact ground space of "frustration-free" Hamiltonians. The complexity of our method is polynomial in the degeneracy of the ground spaces of the Hamiltonians…
In many applications to finite Fermi-systems, the pairing problem has to be treated exactly. We suggest a numerical method of exact solution based on SU(2) quasispin algebras and demonstrate its simplicity and practicality. We show that the…
We present algorithmic improvements for fast and memory-efficient use of discrete spatial symmetries in Exact Diagonalization computations of quantum many-body systems. These techniques allow us to work flexibly in the reduced basis of…
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…
We describe how the methods of group theory (symmetry) are used to optimize the problem of exact diagonalization of a quantum system on a 16-site pyrochlore lattice. By analytically constructing a complete set of symmetrized states, we…
In this work, we present the ``EP code" (version 1.0), a user-friendly and robust computational tool. It computes the exact pairing eigenvalues and eigenvectors directly from the general nuclear pairing Hamiltonian, represented using SU(2)…
The exact solution of proton-neutron isoscalar-isovector (T=0,1) pairing Hamiltonian with non-degenerate single-particle orbits and equal pairing strengths (g_{T=1}= g_{T=0}) is presented for the first time. The Hamiltonian is a particular…
Spin Hamiltonians, like the Heisenberg model, are used to describe magnetic properties of exchange-coupled molecules and solids. For finite clusters, physical quantities such as heat capacities, magnetic susceptibilities or…
While either spin or point-group adaptation is straightforward when considered independently, the standard technique for factoring isotropic spin Hamiltonians by the total spin S and the irreducible representation of the point-group is…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of 2D scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary…
Exploiting inherent symmetries is a common and effective approach to speed up the simulation of quantum systems. However, efficiently accounting for non-Abelian symmetries, such as the $SU(2)$ total-spin symmetry, remains a major challenge.…