Journal Article: Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: a path for the optimization of low-energy many-body basis expansions

Title: Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: a path for the optimization of low-energy many-body basis expansions

The self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo J. Chem. Phys. {\bf 136}, 204101 (2012)] and some ideas of the correlation function Monte Carlo approach [D. M. Ceperley and B. Bernu, J. Chem. Phys. {\bf 89}, 6316 (1988)] are blended to obtain a method for the calculation of thermodynamic properties of many-body systems at low temperatures. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric trial wave functions. A statistical method is derived for the calculation of finite temperature properties of many-body systems near the ground state. In the process we also obtain a parallel algorithm that optimizes the many-body basis of a small subspace of the many-body Hilbert space. This small subspace is optimized to have maximum overlap with the one expanded by the lower energy eigenstates of a many-body Hamiltonian. We show in a model system that the Helmholtz free energy is minimized within this subspace as the iteration number increases. We show that the subspace expanded by the small basis systematically converges towards the subspace expanded by the lowest energy eigenstates. Possible applications of this method to calculate the thermodynamicmore » properties of many-body systems near the ground state are discussed. The resulting basis can be also used to accelerate the calculation of the ground or excited states with Quantum Monte Carlo.« less