Self-Energy Embedding Theory (SEET) for Periodic Systems

Abstract

We present an implementation of the self-energy embedding theory (SEET) for periodic systems and provide a fully self-consistent embedding solution for a simple realistic periodic problem -1D crystalline hydrogen -that displays many of the features present in complex real materials. For this system, we observe a remarkable agreement between our finite temperature periodic implementation results and well established and accurate zero temperature auxiliary quantum Monte Carlo data extrapolated to thermodynamic limit. We discuss differences and similarities with other Green's function embedding methods and provide the detailed algorithmic steps crucial for highly accurate and reproducible results.

Slope invariant T -linear resistivity from local self-energy

“…This argument is useful from a formal perspective but offers little insight into T -linear resistivity at intermediate temperatures or the lack of slope change across the crossover T ∼ U . In this "weak coupling" limit, we approximate single-site DMFT using self-consistent second-order perturbation theory (GF2) [34][35][36][37]. Unlike bare second-order perturbation theory, GF2 is -derivable [38] and therefore thermodynamically consistent and symmetry conserving [39,40], implying that thermodynamic relations and conservation laws are intrinsically satisfied.…”

Projected site-occupation embedding theory

“…This is different in P-SOET, which is split in two different part: the KS problem [Eq. (20)] and the embedded problem [Eq. (24)] obtained by projection of the effective Hamiltonian [Eq.…”

“…The strategy of embedding techniques consists in solving only a small part of the system (referred to as the fragment) by a high-level method, while a low-level approximation is used for the rest of the system (referred to as the environment). Green-function-based methods have been developed, such as the widely used dynamical mean-field theory (DMFT) [7][8][9][10][11][12][13] or the more recent self-energy embedding theory (SEET) [14][15][16][17][18][19][20] . If one is interested about ground-state properties only, the Green function can be replaced by frequency-independent variables, such as the one-particle reduced density matrix (1RDM) or the electron density.…”

Sparse sampling approach to efficient ab initio calculations at finite temperature

“…Applications to low-energy effective model Hamiltonians include lattice Monte Carlo [5], dynamical mean-field theory [6] with its cluster [7], multi-orbital extensions [8,9], and diagrammatic extensions [10][11][12], and diagrammatic or continuous-time quantum Monte Carlo methods [13,14]. In the context of ab initio calculations of correlated materials, examples include the GW method [15][16][17][18][19][20][21][22][23], the self-consistent second order approximation (GF2) [24][25][26][27][28][29][30][31], variants of the dynamical mean field theory [8,[32][33][34][35][36], and the self-energy embedding theory [37][38][39][40][41][42][43].…”