Numerical Diagonalization of Quantum Spin Hamiltonians

Quantum graphs with spin Hamiltonians

The article surveys quantization schemes for metric graphs with spin. Typically quantum graphs are defined with the Laplace or Schrödinger operator which describe particles whose intrinsic angular momentum (spin) is zero. However, in many applications, for example modeling an electron (which has spin-1/2) on a network of thin wires, it is necessary to consider operators which allow spin-orbit i...

Quantum Critical Behavior of the Infinite-range Transverse Ising Spin Glass : An Exact Numerical Diagonalization Study

We report exact numerical diagonalization results of the infinite-range Ising spin glass in a transverse field Γ at zero temperature. Eigenvalues and eigenvectors are determined for various strengths of Γ and for system sizes N ≤ 16. We obtain the moments of the distribution of the spin-glass order parameter, the spin-glass susceptibility and the mass gap at different values of Γ. The disorder ...

Spin dynamics in a double quantum dot: Exact diagonalization study

Maximally Efficient Symmetry Group Founded Diagonalization of Biophysical and Quantum Chemical Hamiltonians

We show that modified Wigner projector technique and generalized Bloch theorem approach yield maximally efficient diagonalization of the Hamiltonian of the large symmetrical systems. For the sake of illustration, we perform a case study of the simplified DNA molecule model and solve the energy eigenproblem analytically by using the unit symmetry cell (symcell) and the corresponding low-dimensio...

Quantum ergodicity for Pauli Hamiltonians with spin 1/2

Quantum ergodicity, which expresses the semiclassical convergence of almost all expectation values of observables in eigenstates of the quantum Hamiltonian to the corresponding classical microcanonical average, is proven for non-relativistic quantum particles with spin 1/2. It is shown that quantum ergodicity holds, if a suitable combination of the classical translational dynamics and the spin ...