Efficient and exact computation of Hubbard and t- J models using quantum diagonalization method

Abstract

The quantum Monte Carlo diagonalization or stochastic diagonalization serves as a computational method of solving exactly quantum Hamiltonian models. While based on a variational method, in which the solution approaches the optimal eigenstate of a huge Hamiltonian matrix, the diagonalization method in practice has difficulty because of the rapidly increasing number of quantum states. Here, we suggest an improved implementation method of finding the ground state via exact diagonalization of the Hubbard and t- J model Hamiltonians. Achieved is a great increase in the computational capability through an optimized code based on Boolean operations, a reduction of the state space using symmetry properties, and an effective variation on the trial ground state. Our method is restricted mainly by the memory capacity to keep the components of the trial ground state. Carried out on a single PC, the method turns out to find exact solutions in a relatively short time with 10^8~10^9 basis states.