Quantum adiabatic switching

Abstract

The quantum adiabatic theorem is explored as a potentially useful tool for obtaining highly excited eigenstates without requiring the calculation of all lower states. Starting in an eigenstate of some H0, the Hamiltonian is deformed adiabatically to the final H; the state of the system at the final time is an eigenstate of the final H which correlates with the eigenstates of H0. The method is free from the difficulties which are present in classical adiabatic switching, i.e., separatrix crossing (tunneling of both the coordinate space and dynamical type) presents no problem, isolated avoided crossings are accurately reproduced, and final states of the correct symmetry are obtained perforce by starting out with properly symmetrized states of the H0. The key issue concerning the possible utility of the technique is the ability to take large time steps in the propagation. The physical motivation for large time steps is that the spatial change in the wave function over a single period of motion is minor. The time steps possible using either the short iterative Lanczos (SIL) or the split operator (SPO) propagation methods are indeed larger than for a conventional propagation, but not sufficiently large as to make the method practical in the general case without further modifications.