Rigorous symmetry adaptation of multiorbital rotationally invariant slave-boson theory with application to Hund's rules physics

Abstract

The theory of correlated electron systems on a lattice proves notoriously complicated because of the exponential growth of Hilbert space. Mean-field approaches provide valuable insight when the self-energy has a dominant local structure. Additionally, the extraction of effective low-energy theories from the generalized many-body representation is highly desirable. In this respect, the rotational-invariant slave boson (RISB) approach in its mean-field formulation enables versatile access to correlated lattice problems. However in its original form, due to numerical complexity, the RISB approach is limited to about three correlated orbitals per lattice site. We thus present a thorough symmetry-adapted advancement of RISB theory, suited to efficiently deal with multi-orbital Hubbard Hamiltonians for complete atomic-shell manifolds. It is utilized to study the intriguing problem of Hund's physics for three-and especially five-orbital manifolds on the correlated lattice, including crystal-field terms as well as spin-orbit interaction. The well-known Janus-face phenomenology, i.e. strenghtening of correlations at smaller-to-intermediate Hubbard U accompanied by a shift of the Mott transition to a larger U value, has a stronger signature and more involved multiplet resolution for five-orbital problems. Spin-orbit interaction effectively reduces the critical local interaction strength and weakens the Janus-face behavior. Application to the realistic challenge of Fe chalcogenides underlines the subtle interplay of the orbital degrees of freedom in these materials. U J H /U = 0.0 J H /U = 0.1 J H /U = 0.2 J H /U = 0.3 J H /U = 0.4 J H /U = 0.7 U J H /U = 0.0 J H /U = 0.1 J H /U = 0.2 J H /U = 0.3 J H /U = 0.4 J H /U = 0.7

Spin-orbit coupling and correlations in three-orbital systems

“…7. As a consequence, the Hund's tail disappears (this was earlier noted also in a rotationally-invariant slave boson study of a five orbital problem [45]), as highlighted in Fig. 6, and the quasiparticle weight increases with SOC in the case of a small U and large Hund's couplings [see Fig.…”

“…Notably, Ref. [45] that studied a five orbital problem also found the disappearance of the Hund's metal tail due to the SOC. This paper is structured as follows.…”

“…In an important work Kim et al looked at the semicircular model [44], as in the present work but did not systematically investigate the evolution of the quasiparticle residue. The effects of the SOC were studied also with the rotationally invariant slave boson methods [45,46]. Notably, Ref.…”

Rotationally invariant slave-boson and density matrix embedding theory: Unified framework and comparative study on the one-dimensional and two-dimensional Hubbard model

“…Another important theoretical method widely used for studying strongly correlated electron systems is the rotationally-invariant slave-boson theory (RISB) [17][18][19] , which is equivalent to the multi-orbital Gutzwiller approximation at the mean-field level [20][21][22] and generally provides predictions almost as accurate as DMFT 19,[23][24][25][26][27][28][29] (especially for the ground-state properties) while being much less computationally demanding. Even if the foundation of the RISB mean-field theory is based on seemingly distinct ideas, it turns out that also this framework can be viewed as a quantum-embedding theory.…”

Hund’s metal regimes and orbital selective Mott transitions in three band systems

“…To that aim we perform rotationally invariant slave-boson mean field theory (RISB) calculations (Lechermann et al 2007, Ferrero, Cornaglia, De Leo, Parcollet, Kotliar & Georges 2009), within the single-site dynamical mean field theory (DMFT) approximation (Georges & Kotliar 1992, Georges et al 1996. The RISB method has proven to be a fast and reliable impurity solver for DMFT equations in the metallic phase, being able to capture Hund's metal physics (Facio et al 2017, Piefke & Lechermann 2018 and to describe OSMTs (Ferrero, Cornaglia, De Leo, Parcollet, Kotliar & Georges 2009).…”