Multiboson exchange embedding for the Hubbard model

In condensed matter physics, strongly correlated electrons are paradigmatic examples of quantum many-body systems that defy a description in terms of simple band theory due to their strong interactions with each other and with the atomic lattice. Their study is both exciting and challenging, not only because the construction of accurate theoretical models requires the consideration of many different factors, such as spin, charge, and orbital degrees of freedom, but also because of the scarcity of exactly solvable reference Hamiltonians. For example, the single-band Hubbard model in more than one dimension has remained at the forefront of computational condensed matter physics for decades, although in many respects it can be regarded as the simplest incarnation of a reasonably realistic correlated electron system.

We present a novel quantum-embedding approach based on the single-boson exchange (SBE) decomposition of the parquet equations. In the SBE formalism, all diagrams contributing to the two-particle vertex F are grouped according to their interaction reducibility, i.e. the way in which they can be split into disconnected parts by removing a bare vertex. This way, unphysical divergences in two-particle irreducible quantities are efficiently mitigated and only the well-conditioned multiboson vertex M is needed to determine all other (single-boson and single-particle) functions self-consistently. Using the dynamical cluster approximation (DCA) with statistically exact CT-QMC simulations, we determine M for small Hubbard clusters coupled to a metallic environment and solve the self-consistent equations on periodic lattices with up to 24 x 24 sites, preserving the full frequency and momentum dependence of all single-boson exchange diagrams. We benchmark our approach against established many-body methods for the half-filled square lattice Hubbard model.