Abstract
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 thermodynamic 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.
