Accurate Formula for the Macroscopic Polarization of Strongly Correlated Materials

Abstract

The many-body Berry phase formula for macroscopic polarization is approximated by a sum of natural orbital geometric phases with fractional occupation numbers accounting for the dominant correlation effects. This formula accurately reproduces the exact polarization in the Rice−Mele−Hubbard model across the band insulator−Mott insulator transition. A similar formula based on a reduced Berry curvature accurately predicts the interaction-induced quenching of Thouless topological charge pumping.

On the time evolution of fermionic occupation numbers

“…Recently, it has been suggested that the generalized Pauli constraints may facilitate the development of more accurate functionals within density-matrix functional theory [41][42][43] . Since quasipinning (say, D j (n) ≈ 0) is approximately observed for several ground states, the quasipinning "mechanism" has attracted some attention in quantum chemistry and quantum-information theory [44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60] .…”

Model Hamiltonian for strongly correlated systems: Systematic, self-consistent, and unique construction

“…Even in cases where it is not possible to cleanly disentangle the bands, there may still be advantages to using the natural Bloch orbitals or natural Wannier functions [151], as opposed to mean-field Bloch orbitals or meanfield Wannier functions, in selecting a subset of degrees of freedom to treat at a higher level of theory. Natural Bloch orbitals are intrinsic variables of the system, being defined in terms of the one-body reduced density matrix, a quantity obtained by simply tracing out degrees of freedom-a linear operation-and may therefore provide a more suitable starting point than mean-field Bloch orbitals in strongly correlated systems.…”

“…Smooth and continuous natural occupation num- ber bands and natural Bloch orbitals in the true Brillouin zone of the crystal are defined, as described in Ref. 151, by unfolding the bands obtained from the full many-body wavefunction under twisted boundary conditions [41,42] or, equivalently, artificial magnetic fields [166]. If we express the Hubbard interactions in Eq.…”

“…Our theory provides a practical way to make ab initio calculations of geometric and topological properties in strongly correlated systems. It has recently been shown that the natural Bloch orbitals, natural occupation numbers and their conjugate phases, which combine to form a set of natural orbital geometric phases, contain most of the information about the effects of many-body correlations on geometric and topological quantities in the Rice-Mele-Hubbard model [151]. Since these variables are included in our theory through the self-consistent solution of the many-body lattice model and a generalized Kohn-Sham equation, we expect to obtain accurate results for geometric and topological quantities in real systems.…”

“…In contrast, the natural occupation numbers form exact, unbroadened bands irrespective of the interaction strength. Hence, topological invariants calculated in terms of the natural Bloch orbitals are precisely quantized [151]. Quantum Monte Carlo methods have been used to evaluate many-body topological invariants in correlated model systems [152].…”