Iterative backflow renormalization procedure for many-body ground-state wave functions of strongly interacting normal Fermi liquids

Abstract

We show how a ground state trial wavefunction of a Fermi liquid can be systematically improved introducing a sequence of renormalized coordinates through an iterative backflow transformation. We apply this scheme to calculate the ground state energy of liquid 3 He in two dimensions at freezing density using variational and fixed-node diffusion Monte Carlo. Comparing with exact transient estimate results for systems with small number of particles, we find that variance extrapolations provide accurate results for the true ground state together with stringent lower bounds. For larger systems these bounds can in turn be used to quantify the systematic bias of fixed-node calculations. These wave functions are size consistent and the scaling of their computational complexity with the number of particles is the same as for standard backflow wave functions.

Variational and diffusion quantum Monte Carlo calculations with the CASINO code

“…Our lowest VMC energy corresponds to 99.53(2)% of the binding energy of Ps 2 . Since the exact wave function is nodeless, an extrapolation to zero VMC variance 54 can be expected to yield a reasonable estimate of the ground-state energy. We find that this extrapolated energy accounts for 99.94(2)% of the binding energy of Ps 2 .…”

Two-dimensional mixture of dipolar fermions: Equation of state and magnetic phases

“…As observed above, the fixed-node bias cannot be neglected in the study of itinerant ferromagnetism. In this section we investigate this issue in detail, by making use of improved trial wave functions based on the iterative backflow transformations [52].…”

“…In this work, we employ the DMC method for the case of a twodimensional dipolar gas, and we show that the level of accuracy obtained with the commonly used Jastrow-Slater and backflow-corrected trial wave functions is not sufficient to determine whether the ground state becomes polarized. To go beyond this limitation, we make use of the recently-developed iterative-backflow trial wave functions [52,53], finding no signature of a polarized ground state.…”

Backflow Transformations via Neural Networks for Quantum Many-Body Wave Functions

“…Early attempts for writing down variational Fermion wave-functions, such as Slater determinants [3] and BCS wave-functions [4], focused on finding the ground state of a mean field Hamiltonian which best matched the interacting ground state. Since these early attempts more sophisticated wave-functions have been developed which dress these mean-field starting points including Slater-Jastrow [5,6], Slater-Jastrow-Backflow [1,7] and iterative backflow [8] which has recently been described as a non-linear network [9]. These wave-functions have the advantage that the mean-field starting point can directly incorporate the basic physics of the problem.…”