Equivalence of Gutzwiller and slave-boson mean-field theories for multiband Hubbard models

Abstract

We demonstrate that a recently introduced slave-boson mean-field theory is equivalent to our Gutzwiller theory for multi-band Hubbard models with general onsite interactions. We relate the different objects that appear in both approaches at zero temperature and discuss the limitations of both methods.

Phase Diagram and Electronic Structure of Praseodymium and Plutonium

“…(32) and (33) to compute the Lagrange multipliers μ and η and the corresponding jΨ 0 i, which determines n (37)], which determine the left sides of Eqs. (38) and (39). Equations (38) and (39) are verified if and only if ðR; λÞ is the correct set of variational parameters.…”

“…(38) and (39). Equations (38) and (39) are verified if and only if ðR; λÞ is the correct set of variational parameters.…”

“…The GA approximation was, thereafter, extensively developed [21][22][23][24][25][26][27], and it has been formulated and implemented in combination with realistic electronic structure calculations such as the LDA þ GA approach [23,28], which has been applied successfully to many systems [29][30][31][32][33][34][35][36]. A third important many-body technique is the slave boson approach (SB) [37,38], which is, in principle, an exact reformulation of the quantum many-body problem for model Hamiltonians, and it reproduces the results of the GA at the saddle-point level [24,39]. This technique has recently been extended to treat full rotationally invariant interactions [38,40], and it has also been combined with LDA for the study of real materials, either in the form of impurity solvers for the resulting LDA þ DMFT impurity models (LDA þ DMFTþ SB) [6,41] or directly on the lattice [42]-which are equivalent approaches, as we will show.…”

Field effect on surface states in a doped Mott-insulator thin film

“…For heterostructures, GA was found to be in good qualitative agreement with the more refined DMFT method for the half filled case 9 . While GA and SBMFT are equivalent for zero temperature 12 , in two site DMFT, like GA, the bulk QP weight is governed by a simple power law and there is only a correction to U c when compared with the linearized DMFT 13,14 . Generally, GA over-estimates the QP weight at all dopings but it is considered to be accurate enough to describe low energy excitations and is routinely used for interpolations in combination with DMFT methods 2 .…”

Slave Boson Theory of Orbital Differentiation with Crystal Field Effects: Application toUO2

“…In this work we address the orbital differentiation problem from an ab-initio perspective using the rotationally invariant slave boson (RISB) mean-field theory [8][9][10]. As we demonstrate, this method can be derived from an exact operatorial reformulation of the many-body problem, which reproduces the Gutzwiller approximation [11] at the mean-field level [12,13] and constitutes a starting point to calculate further corrections. By exploiting the gauge symmetry of the RISB theory, we build efficient systematic algorithms which enable us to solve the mean-field equations and elucidate the pattern of orbital differentiation even in lowsymmetry 5f electron systems.…”