Density matrix renormalization group approach to two-fluid open many-fermion systems

Abstract

We have extended the density matrix renormalization group (DMRG) approach to two-fluid open manyfermion systems governed by complex-symmetric Hamiltonians. The applications are carried out for three-and four-nucleon (proton-neutron) systems within the Gamow shell model (GSM) in the complex-energy plane. We study necessary and sufficient conditions for the GSM+DMRG method to yield the correct ground-state eigenvalue and discuss different truncation schemes within the DMRG. The proposed approach will enable configuration interaction studies of weakly bound and unbound strongly interacting complex systems, which, because of a prohibitively large size of Fock space, cannot be treated by means of the direct diagonalization.

Ab initiono-core Gamow shell model calculations with realistic interactions

“…These are expressed as linear combination of the vectors |i P in P and all matrix elements of the suboperators in these optimized states are recalculated and stored. Note that at each step, we enforce that at least one state in each family {n; j π P } is kept [70]. The warm-up phase continues by having the P subspace grow by adding scattering shells one by one until the last shell is reached, providing a first guess for the wave function of the system in the whole ensemble of shells.…”

“…In this paper, all nucleons are considered active and realistic two-body interactions are used but nevertheless, the application of the DMRG method is similar. In the following, we recall the main ideas of the DMRG in the multi-shell GSM problem [70].…”

“…In this paper, we have used one of these methods, namely, the DMRG method [67,68] which has been generalized in the context of the GSM in [69,70]. The GSM/DMRG approach has been applied previously to study several weakly-bound/unbound nuclei described as few-valence-nucleon systems interacting via schematic two-body forces above an inert core.…”

“…For three-particles systems we can perform an exact diagonalization using the Lanczos method and, therefore, we can test the precision of the NCGSM/DMRG approach. Since details of the DMRG algorithm can be found in [70], we only mention the basic ingredients of the DMRG calculation.…”

New applications of renormalization group methods in nuclear physics

“…[93], the No-Core Gamow Shell Model (NCGSM), which treats bound, resonant, and scattering states equally, was first applied to study some well-bound and unbound states of the helium isotopes [93]. The density matrix renormalization group (DMRG) method [94] was used to solve the many-body Schrödinger equation. The V low k RG was used to decouple high from low momentum to improve the convergence of the calculations.…”